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Analysis in Banach Spaces : Volume III: Harmonic Analysis and Spectral Theory / / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
| Analysis in Banach Spaces : Volume III: Harmonic Analysis and Spectral Theory / / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis |
| Autore | Hytönen Tuomas |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (839 pages) |
| Disciplina | 515.732 |
| Altri autori (Persone) |
van NeervenJan
VeraarMark WeisLutz |
| Collana | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Soggetto topico |
Functional analysis
Fourier analysis Harmonic analysis Operator theory Mathematical analysis Functional Analysis Fourier Analysis Abstract Harmonic Analysis Operator Theory Analysis Anàlisi harmònica Teoria d'operadors Anàlisi de Fourier Anàlisi matemàtica Anàlisi funcional Espais de Banach |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-46598-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 11 Singular integral operators -- 12 Dyadic operators and the T (1) theorem -- 13 The Fourier transform and multipliers -- 14 Function spaces -- 15 Bounded imaginary powers -- 16 The H∞-functional calculus revisited -- 17 Maximal regularity -- 18 Nonlinear parabolic evolution equations in critical spaces -- Appendix Q: Questions -- Appendix K: Semigroup theory revisited -- Appendix L: The trace method for real interpolation theory. |
| Record Nr. | UNINA-9910770276503321 |
Hytönen Tuomas
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Basic monotonicity methods with some applications / / Marek Galewski
| Basic monotonicity methods with some applications / / Marek Galewski |
| Autore | Galewski Marek |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (183 pages) |
| Disciplina | 515.353 |
| Collana | Compact Textbooks in Mathematics |
| Soggetto topico |
Monotone operators
Teoria d'operadors |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-75308-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466394703316 |
|
Galewski Marek
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Basic monotonicity methods with some applications / / Marek Galewski
| Basic monotonicity methods with some applications / / Marek Galewski |
| Autore | Galewski Marek |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (183 pages) |
| Disciplina | 515.353 |
| Collana | Compact Textbooks in Mathematics |
| Soggetto topico |
Monotone operators
Teoria d'operadors |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-75308-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910495219503321 |
|
Galewski Marek
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Completeness theorems and characteristic Matrix functions : applications to integral and differential operators / / Marinus A. Kaashoek and Sjoerd M. Verduyn Lunel
| Completeness theorems and characteristic Matrix functions : applications to integral and differential operators / / Marinus A. Kaashoek and Sjoerd M. Verduyn Lunel |
| Autore | Kaashoek M. A. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] |
| Descrizione fisica | 1 online resource (358 pages) |
| Disciplina | 515.733 |
| Collana | Operator theory, advances and applications |
| Soggetto topico |
Hilbert space
Operator theory Teoria d'operadors Espais de Hilbert |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-04508-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910574861903321 |
|
Kaashoek M. A.
|
||
| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Completeness theorems and characteristic Matrix functions : applications to integral and differential operators / / Marinus A. Kaashoek and Sjoerd M. Verduyn Lunel
| Completeness theorems and characteristic Matrix functions : applications to integral and differential operators / / Marinus A. Kaashoek and Sjoerd M. Verduyn Lunel |
| Autore | Kaashoek M. A. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] |
| Descrizione fisica | 1 online resource (358 pages) |
| Disciplina | 515.733 |
| Collana | Operator theory, advances and applications |
| Soggetto topico |
Hilbert space
Operator theory Teoria d'operadors Espais de Hilbert |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-04508-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996479371603316 |
|
Kaashoek M. A.
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| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computation and approximation / / Vijay Gupta, Michael Th Rassias
| Computation and approximation / / Vijay Gupta, Michael Th Rassias |
| Autore | Gupta Vijay |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (107 pages) |
| Disciplina | 511.4 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Approximation theory
Operator theory Teoria d'operadors Teoria de l'aproximació |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-85563-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466556703316 |
|
Gupta Vijay
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computation and approximation / / Vijay Gupta, Michael Th Rassias
| Computation and approximation / / Vijay Gupta, Michael Th Rassias |
| Autore | Gupta Vijay |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (107 pages) |
| Disciplina | 511.4 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Approximation theory
Operator theory Teoria d'operadors Teoria de l'aproximació |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-85563-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910510566303321 |
|
Gupta Vijay
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Counterexamples in operator theory / / Mohammed Hichem Mortad
| Counterexamples in operator theory / / Mohammed Hichem Mortad |
| Autore | Mortad Mohammed Hichem <1978-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (613 pages) |
| Disciplina | 515.724 |
| Soggetto topico |
Operator theory
Teoria d'operadors |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030978143
9783030978136 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I Bounded Linear Operators -- 1 Some Basic Properties -- 1.1 Basics -- 1.2 Questions -- 1.2.1 Does the ``Banachness'' of B(X,Y) Yield That of Y? -- 1.2.2 An Operator A≠0 with A2=0 and So "026B30D A2"026B30D ≠"026B30D A"026B30D 2 -- 1.2.3 A,BB(H) with ABAB=0 but BABA≠0 -- 1.2.4 An Operator Commuting with Both A+B and AB, But It Does Not Commute with Any of A and B -- 1.2.5 The Non-transitivity of the Relation of Commutativity -- 1.2.6 Two Operators A,B with "026B30D AB-BA"026B30D =2"026B30D A"026B30D "026B30D B"026B30D -- 1.2.7 Two Nilpotent Operators Such That Their Sum and Their Product Are Not Nilpotent -- 1.2.8 Two Non-nilpotent Operators Such That Their Sum and Their Product Are Nilpotent -- 1.2.9 An Invertible Operator A with "026B30D A-1"026B30D ≠1/"026B30D A"026B30D -- 1.2.10 An AB(H) Such That I-A Is Invertible and Yet "026B30D A"026B30D ≥1 -- 1.2.11 Two Non-invertible A,BB(H) Such That AB Is Invertible -- 1.2.12 Two A,B Such That A+B=AB but AB≠BA -- 1.2.13 Left (Resp. Right) Invertible Operators with Many Left (Resp. Right) Inverses -- 1.2.14 An Injective Operator That Is Not Left Invertible -- 1.2.15 An A≠0 Such That "426830A Ax,x"526930B =0 for All xH -- 1.2.16 The Open Mapping Theorem Fails to Hold True for Bilinear Mappings -- Answers -- 2 Basic Classes of Bounded Linear Operators -- 2.1 Basics -- 2.2 Questions -- 2.2.1 A Non-unitary Isometry -- 2.2.2 A Nonnormal A Such That kerA=kerA* -- 2.2.3 Do Normal Operators A and B Satisfy "026B30D ABx"026B30D ="026B30D BAx"026B30D for All x? -- 2.2.4 Do Normal Operators A and B Satisfy "026B30D ABx"026B30D ="026B30D AB*x"026B30D for All x? -- 2.2.5 Two Operators B and V Such That "026B30D BV"026B30D ≠"026B30D B"026B30D Where V Is an Isometry -- 2.2.6 An Invertible Normal Operator That Is not Unitary.
2.2.7 Two Self-Adjoint Operators Whose Product Is Not Even Normal -- 2.2.8 Two Normal Operators A,B Such That AB Is Normal, but AB≠BA -- 2.2.9 Two Normal Operators Whose Sum Is Not Normal -- 2.2.10 Two Unitary U,V for Which U+V Is Not Unitary -- 2.2.11 Two Anti-commuting Normal Operators Whose Sum Is Not Normal -- 2.2.12 Two Unitary Operators A and B Such That AB, BA, and A+B Are All Normal yet AB≠BA -- 2.2.13 A Non-self-adjoint A Such That A2 Is Self-Adjoint -- 2.2.14 Three Self-Adjoint Operators A, B, and C Such That ABC Is Self-Adjoint, Yet No Two of A, B, and C Need to Commute -- 2.2.15 An Orthogonal Projection P and a Normal A Such That PAP Is Not Normal -- 2.2.16 A Partial Isometry That Is Not an Isometry -- 2.2.17 A Non-partial Isometry V Such That V2 Is a Partial Isometry -- 2.2.18 A Partial Isometry V Such That V2 Is a Partial Isometry, but Neither V3 Nor V4 Is One -- 2.2.19 No Condition of U=U*, U2=I and U*U=I Needs to Imply Any of the Other Two -- 2.2.20 A B Such That BB*+B*B=I and B2=B*2=0 -- 2.2.21 A Nonnormal Solution of (A*A)2=A*2A2 -- 2.2.22 An AB(H) Such That An=I, While An-1≠I, n≥2 -- 2.2.23 A Unitary A Such That An≠I for All nN, n≥2 -- 2.2.24 A Normal Non-self-adjoint Operator AB(H) Such That A*A=An -- 2.2.25 A Nonnormal A Satisfying A*pAq=An -- Answers -- 3 Operator Topologies -- 3.1 Questions -- 3.1.1 Strong Convergence Does Not Imply Convergence in Norm, and Weak Convergence Does Not Entail Strong Convergence -- 3.1.2 s-limn∞ An=As-limn∞ A*n=A* -- 3.1.3 (A,B)AB Is Not Weakly Continuous -- 3.1.4 The Uniform Limit of a Sequence of Invertible Operators -- 3.1.5 A Sequence of Self-adjoint Operators Such That None of Its Terms Commutes with the (Uniform) Limit of the Sequence -- 3.1.6 Strong (or Weak) Limit of Sequences of Unitary or Normal Operators -- Answers -- 4 Positive Operators -- 4.1 Basics -- 4.2 Questions. 4.2.1 Two Positive Operators A,B Such That AB=0 -- 4.2.2 Two A,B Such That A≤0, A≥0, B≤0, B≥0, yet AB≥0 -- 4.2.3 KAK*≤A Where A≥0 and K Is a Contraction -- 4.2.4 KAK*≤A AK=KA Where A≥0 and K Is an Isometry -- 4.2.5 KAK*≤A AK*=KA Where A≥0 and K Is Unitary -- 4.2.6 The Operator Norm Is Not Strictly Increasing -- 4.2.7 A≥B≥0A2≥B2 -- 4.2.8 A,B≥0AB+BA≥0 -- 4.2.9 Two Non-self-adjoint A and B Such That An+Bn≥0 for All n -- 4.2.10 Two Positive A,B (with A≠0 and B≠0) and Such That AB≥0 but A2+B2 Is Not Invertible -- 4.2.11 Two A, B Satisfying "026B30D AB-BA"026B30D =1/2"026B30D A"026B30D "026B30D B"026B30D -- 4.2.12 Two A, B Satisfying "026B30D AB-BA"026B30D ="026B30D A"026B30D "026B30D B"026B30D -- 4.2.13 On Normal Solutions of the Equations AA*=qA*A, qR -- Answers -- 5 Matrices of Bounded Operators -- 5.1 Basics -- 5.2 Questions -- 5.2.1 A Non-invertible Matrix Whose Formal Determinant Is Invertible -- 5.2.2 An Invertible Matrix Whose Formal Determinant Is Not Invertible -- 5.2.3 Invertible Triangular Matrix vs. Left and Right Invertibility of Its Diagonal Elements -- 5.2.4 Non-invertible Triangular Matrix vs. Left and Right Invertibility of Its Diagonal Elements -- 5.2.5 An Invertible Matrix yet None of Its Entries Is Invertible -- 5.2.6 A Normal Matrix yet None of Its Entries Is Normal -- 5.2.7 A Unitary Matrix yet None of Its Entries Is Unitary -- 5.2.8 Two Non-comparable Self-Adjoint Matrices yet the Corresponding Entries Are Comparable -- 5.2.9 An Isometry S Such That S2 Is Unitarily Equivalent to SS -- 5.2.10 An Infinite Direct Sum of Invertible Operators Need Not Be Invertible -- 5.2.11 The Similarity of AB to CD Does Not Entail the Similarity of A to C or That of B to D -- 5.2.12 A Matrix of Operators T on H2 Such That T3=0 But T2≠0 -- 5.2.13 Block Circulant Matrices Are Not Necessarily Circulant -- Answers -- 6 (Square) Roots of Bounded Operators. 6.1 Basics -- 6.2 Questions -- 6.2.1 A Self-Adjoint Operator with an Infinitude of Self-Adjoint Square Roots -- 6.2.2 An Operator Without Any Square Root -- 6.2.3 A Nilpotent Operator with Infinitely Many Square Roots -- 6.2.4 An Operator Having a Cube Root but Without Any Square Root -- 6.2.5 An Operator Having a Square Root but Without Any Cube Root -- 6.2.6 A Non-invertible Operator with Infinitely Many Square Roots -- 6.2.7 An Operator A Without Any Square Root, but A+αI Always Has One (αC*) -- 6.2.8 A2≥0A≥0 Even When A Is Normal -- 6.2.9 A3≥0A≥0 Even When A Is Normal -- 6.2.10 An Operator Having Only Two Square Roots -- 6.2.11 Can an Operator Have Only One Square Root? -- 6.2.12 Can an Operator Have Only Two Cube Roots? -- 6.2.13 A Rootless Operator -- 6.2.14 On Some Result By B. Yood on Rootless Matrices -- 6.2.15 A Non-nilpotent Rootless Matrix -- 6.2.16 Two (Self-Adjoint) Square Roots of a Self-Adjoint Operator Need Not Commute -- 6.2.17 A BB(H) Commuting with A Need Not Commute with an Arbitrary Root of A -- 6.2.18 A Self-Adjoint Operator Without Any Positive Square Root -- 6.2.19 Three Positive Operators A,B,CB(H) Such That A≥B≥0 and C Is Invertible Yet (CA2C)12≥(CB2C)12 -- 6.2.20 Three Positive Operators A,B,CB(H) Such That A≤C and B≤C Yet (A2+B2)12 ≤2 C -- 6.2.21 On Some Result by F. Kittaneh on Normal Square Roots -- 6.2.22 On the Normality of Roots of Normal Operators Having Co-prime Powers -- 6.2.23 An Isometry Without Square or Cube Roots -- 6.2.24 Two Operators A and B Without Square Roots, Yet AB Has a Square Root -- Answers -- 7 Absolute Value, Polar Decomposition -- 7.1 Basics -- 7.2 Questions -- 7.2.1 An A Such That |Re A|≤|A| and |`3́9`42`"̇613A``45`47`"603AImA|≤|A| -- 7.2.2 A Weakly Normal T Such That T2 Is Not Normal -- 7.2.3 Two Self-Adjoints A,B Such That |A+B| ≤|A|+|B|. 7.2.4 Two Self-Adjoint Operators A,B That Do Not Satisfy |A||B|+|B||A|≥AB+BA -- 7.2.5 Two Self-Adjoint Operators A and B Such That "026B30D |A|-|B|"026B30D ≤"026B30D A-B"026B30D -- 7.2.6 Two Non-commuting Operators A and B That Are Not Normal and Yet |A+B|=|A|+|B| -- 7.2.7 Two Positive Operators A and B with |A-B|≤A+B -- 7.2.8 Two Self-adjoint Operators A and B Such That I+|AB-I|≤(I+|A-I|)(I+|B-I|) -- 7.2.9 Two Self-Adjoints A,BB(H) Such That |AB|≠|A||B| -- 7.2.10 Two Operators A and B Such That AB=BA, However, |A||B|≠|B||A| -- 7.2.11 A Pair of Operators A and B Such That A|B|=|B|A and B|A|=|A|B, But AB≠BA and AB*≠B*A -- 7.2.12 An Operator A Such That A|A|≠|A|A -- 7.2.13 An A Such That |A||A*|=|A*||A| But AA*≠A*A -- 7.2.14 An Operator A Such That |A2|≠|A|2 -- 7.2.15 A Non-surjective A Such That |A| Is Surjective -- 7.2.16 Two Self-Adjoint Operators A,B with B≥0 Such That -B≤A≤B but |A|≤B -- 7.2.17 The Failure of the Inequality |"426830A Ax,x"526930B |≤"426830A |A|x,x"526930B -- 7.2.18 On the Generalized Cauchy-Schwarz Inequality -- 7.2.19 On the Failure of Some Variants of the Generalized Cauchy-Schwarz Inequality -- 7.2.20 A Sequence of Self-Adjoint Operators (An) Such That "026B30D |An|-|A|"026B30D 0 But "026B30D An-A"026B30D 0 -- 7.2.21 The Non-weakly Continuity of A|A| -- 7.2.22 A Sequence of Operators (An) Converging Strongly to A, but (|An|) Does Not Converge Strongly to |A| -- 7.2.23 An Invertible A=U|A| with U|A|≠|A|U, UA≠AU, and A|A|≠|A|A -- 7.2.24 Left or Right Invertible Operators Do Not Enjoy a (``Unitary'') Polar Decomposition -- 7.2.25 A Normal Operator Whose Polar Decomposition Is Not Unique -- 7.2.26 On a Result of the Uniqueness of the Polar Decomposition By Ichinose-Iwashita -- 7.2.27 An Operator A Expressed as A=V|A| with A3=0 but V3≠0 -- 7.2.28 An Invertible Operator A Expressed as A=U|A| with A3=I but U3≠I -- Answers. 8 Spectrum. |
| Record Nr. | UNISA-996479371003316 |
|
Mortad Mohammed Hichem <1978->
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Counterexamples in operator theory / / Mohammed Hichem Mortad
| Counterexamples in operator theory / / Mohammed Hichem Mortad |
| Autore | Mortad Mohammed Hichem <1978-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (613 pages) |
| Disciplina | 515.724 |
| Soggetto topico |
Operator theory
Teoria d'operadors |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030978143
9783030978136 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I Bounded Linear Operators -- 1 Some Basic Properties -- 1.1 Basics -- 1.2 Questions -- 1.2.1 Does the ``Banachness'' of B(X,Y) Yield That of Y? -- 1.2.2 An Operator A≠0 with A2=0 and So "026B30D A2"026B30D ≠"026B30D A"026B30D 2 -- 1.2.3 A,BB(H) with ABAB=0 but BABA≠0 -- 1.2.4 An Operator Commuting with Both A+B and AB, But It Does Not Commute with Any of A and B -- 1.2.5 The Non-transitivity of the Relation of Commutativity -- 1.2.6 Two Operators A,B with "026B30D AB-BA"026B30D =2"026B30D A"026B30D "026B30D B"026B30D -- 1.2.7 Two Nilpotent Operators Such That Their Sum and Their Product Are Not Nilpotent -- 1.2.8 Two Non-nilpotent Operators Such That Their Sum and Their Product Are Nilpotent -- 1.2.9 An Invertible Operator A with "026B30D A-1"026B30D ≠1/"026B30D A"026B30D -- 1.2.10 An AB(H) Such That I-A Is Invertible and Yet "026B30D A"026B30D ≥1 -- 1.2.11 Two Non-invertible A,BB(H) Such That AB Is Invertible -- 1.2.12 Two A,B Such That A+B=AB but AB≠BA -- 1.2.13 Left (Resp. Right) Invertible Operators with Many Left (Resp. Right) Inverses -- 1.2.14 An Injective Operator That Is Not Left Invertible -- 1.2.15 An A≠0 Such That "426830A Ax,x"526930B =0 for All xH -- 1.2.16 The Open Mapping Theorem Fails to Hold True for Bilinear Mappings -- Answers -- 2 Basic Classes of Bounded Linear Operators -- 2.1 Basics -- 2.2 Questions -- 2.2.1 A Non-unitary Isometry -- 2.2.2 A Nonnormal A Such That kerA=kerA* -- 2.2.3 Do Normal Operators A and B Satisfy "026B30D ABx"026B30D ="026B30D BAx"026B30D for All x? -- 2.2.4 Do Normal Operators A and B Satisfy "026B30D ABx"026B30D ="026B30D AB*x"026B30D for All x? -- 2.2.5 Two Operators B and V Such That "026B30D BV"026B30D ≠"026B30D B"026B30D Where V Is an Isometry -- 2.2.6 An Invertible Normal Operator That Is not Unitary.
2.2.7 Two Self-Adjoint Operators Whose Product Is Not Even Normal -- 2.2.8 Two Normal Operators A,B Such That AB Is Normal, but AB≠BA -- 2.2.9 Two Normal Operators Whose Sum Is Not Normal -- 2.2.10 Two Unitary U,V for Which U+V Is Not Unitary -- 2.2.11 Two Anti-commuting Normal Operators Whose Sum Is Not Normal -- 2.2.12 Two Unitary Operators A and B Such That AB, BA, and A+B Are All Normal yet AB≠BA -- 2.2.13 A Non-self-adjoint A Such That A2 Is Self-Adjoint -- 2.2.14 Three Self-Adjoint Operators A, B, and C Such That ABC Is Self-Adjoint, Yet No Two of A, B, and C Need to Commute -- 2.2.15 An Orthogonal Projection P and a Normal A Such That PAP Is Not Normal -- 2.2.16 A Partial Isometry That Is Not an Isometry -- 2.2.17 A Non-partial Isometry V Such That V2 Is a Partial Isometry -- 2.2.18 A Partial Isometry V Such That V2 Is a Partial Isometry, but Neither V3 Nor V4 Is One -- 2.2.19 No Condition of U=U*, U2=I and U*U=I Needs to Imply Any of the Other Two -- 2.2.20 A B Such That BB*+B*B=I and B2=B*2=0 -- 2.2.21 A Nonnormal Solution of (A*A)2=A*2A2 -- 2.2.22 An AB(H) Such That An=I, While An-1≠I, n≥2 -- 2.2.23 A Unitary A Such That An≠I for All nN, n≥2 -- 2.2.24 A Normal Non-self-adjoint Operator AB(H) Such That A*A=An -- 2.2.25 A Nonnormal A Satisfying A*pAq=An -- Answers -- 3 Operator Topologies -- 3.1 Questions -- 3.1.1 Strong Convergence Does Not Imply Convergence in Norm, and Weak Convergence Does Not Entail Strong Convergence -- 3.1.2 s-limn∞ An=As-limn∞ A*n=A* -- 3.1.3 (A,B)AB Is Not Weakly Continuous -- 3.1.4 The Uniform Limit of a Sequence of Invertible Operators -- 3.1.5 A Sequence of Self-adjoint Operators Such That None of Its Terms Commutes with the (Uniform) Limit of the Sequence -- 3.1.6 Strong (or Weak) Limit of Sequences of Unitary or Normal Operators -- Answers -- 4 Positive Operators -- 4.1 Basics -- 4.2 Questions. 4.2.1 Two Positive Operators A,B Such That AB=0 -- 4.2.2 Two A,B Such That A≤0, A≥0, B≤0, B≥0, yet AB≥0 -- 4.2.3 KAK*≤A Where A≥0 and K Is a Contraction -- 4.2.4 KAK*≤A AK=KA Where A≥0 and K Is an Isometry -- 4.2.5 KAK*≤A AK*=KA Where A≥0 and K Is Unitary -- 4.2.6 The Operator Norm Is Not Strictly Increasing -- 4.2.7 A≥B≥0A2≥B2 -- 4.2.8 A,B≥0AB+BA≥0 -- 4.2.9 Two Non-self-adjoint A and B Such That An+Bn≥0 for All n -- 4.2.10 Two Positive A,B (with A≠0 and B≠0) and Such That AB≥0 but A2+B2 Is Not Invertible -- 4.2.11 Two A, B Satisfying "026B30D AB-BA"026B30D =1/2"026B30D A"026B30D "026B30D B"026B30D -- 4.2.12 Two A, B Satisfying "026B30D AB-BA"026B30D ="026B30D A"026B30D "026B30D B"026B30D -- 4.2.13 On Normal Solutions of the Equations AA*=qA*A, qR -- Answers -- 5 Matrices of Bounded Operators -- 5.1 Basics -- 5.2 Questions -- 5.2.1 A Non-invertible Matrix Whose Formal Determinant Is Invertible -- 5.2.2 An Invertible Matrix Whose Formal Determinant Is Not Invertible -- 5.2.3 Invertible Triangular Matrix vs. Left and Right Invertibility of Its Diagonal Elements -- 5.2.4 Non-invertible Triangular Matrix vs. Left and Right Invertibility of Its Diagonal Elements -- 5.2.5 An Invertible Matrix yet None of Its Entries Is Invertible -- 5.2.6 A Normal Matrix yet None of Its Entries Is Normal -- 5.2.7 A Unitary Matrix yet None of Its Entries Is Unitary -- 5.2.8 Two Non-comparable Self-Adjoint Matrices yet the Corresponding Entries Are Comparable -- 5.2.9 An Isometry S Such That S2 Is Unitarily Equivalent to SS -- 5.2.10 An Infinite Direct Sum of Invertible Operators Need Not Be Invertible -- 5.2.11 The Similarity of AB to CD Does Not Entail the Similarity of A to C or That of B to D -- 5.2.12 A Matrix of Operators T on H2 Such That T3=0 But T2≠0 -- 5.2.13 Block Circulant Matrices Are Not Necessarily Circulant -- Answers -- 6 (Square) Roots of Bounded Operators. 6.1 Basics -- 6.2 Questions -- 6.2.1 A Self-Adjoint Operator with an Infinitude of Self-Adjoint Square Roots -- 6.2.2 An Operator Without Any Square Root -- 6.2.3 A Nilpotent Operator with Infinitely Many Square Roots -- 6.2.4 An Operator Having a Cube Root but Without Any Square Root -- 6.2.5 An Operator Having a Square Root but Without Any Cube Root -- 6.2.6 A Non-invertible Operator with Infinitely Many Square Roots -- 6.2.7 An Operator A Without Any Square Root, but A+αI Always Has One (αC*) -- 6.2.8 A2≥0A≥0 Even When A Is Normal -- 6.2.9 A3≥0A≥0 Even When A Is Normal -- 6.2.10 An Operator Having Only Two Square Roots -- 6.2.11 Can an Operator Have Only One Square Root? -- 6.2.12 Can an Operator Have Only Two Cube Roots? -- 6.2.13 A Rootless Operator -- 6.2.14 On Some Result By B. Yood on Rootless Matrices -- 6.2.15 A Non-nilpotent Rootless Matrix -- 6.2.16 Two (Self-Adjoint) Square Roots of a Self-Adjoint Operator Need Not Commute -- 6.2.17 A BB(H) Commuting with A Need Not Commute with an Arbitrary Root of A -- 6.2.18 A Self-Adjoint Operator Without Any Positive Square Root -- 6.2.19 Three Positive Operators A,B,CB(H) Such That A≥B≥0 and C Is Invertible Yet (CA2C)12≥(CB2C)12 -- 6.2.20 Three Positive Operators A,B,CB(H) Such That A≤C and B≤C Yet (A2+B2)12 ≤2 C -- 6.2.21 On Some Result by F. Kittaneh on Normal Square Roots -- 6.2.22 On the Normality of Roots of Normal Operators Having Co-prime Powers -- 6.2.23 An Isometry Without Square or Cube Roots -- 6.2.24 Two Operators A and B Without Square Roots, Yet AB Has a Square Root -- Answers -- 7 Absolute Value, Polar Decomposition -- 7.1 Basics -- 7.2 Questions -- 7.2.1 An A Such That |Re A|≤|A| and |`3́9`42`"̇613A``45`47`"603AImA|≤|A| -- 7.2.2 A Weakly Normal T Such That T2 Is Not Normal -- 7.2.3 Two Self-Adjoints A,B Such That |A+B| ≤|A|+|B|. 7.2.4 Two Self-Adjoint Operators A,B That Do Not Satisfy |A||B|+|B||A|≥AB+BA -- 7.2.5 Two Self-Adjoint Operators A and B Such That "026B30D |A|-|B|"026B30D ≤"026B30D A-B"026B30D -- 7.2.6 Two Non-commuting Operators A and B That Are Not Normal and Yet |A+B|=|A|+|B| -- 7.2.7 Two Positive Operators A and B with |A-B|≤A+B -- 7.2.8 Two Self-adjoint Operators A and B Such That I+|AB-I|≤(I+|A-I|)(I+|B-I|) -- 7.2.9 Two Self-Adjoints A,BB(H) Such That |AB|≠|A||B| -- 7.2.10 Two Operators A and B Such That AB=BA, However, |A||B|≠|B||A| -- 7.2.11 A Pair of Operators A and B Such That A|B|=|B|A and B|A|=|A|B, But AB≠BA and AB*≠B*A -- 7.2.12 An Operator A Such That A|A|≠|A|A -- 7.2.13 An A Such That |A||A*|=|A*||A| But AA*≠A*A -- 7.2.14 An Operator A Such That |A2|≠|A|2 -- 7.2.15 A Non-surjective A Such That |A| Is Surjective -- 7.2.16 Two Self-Adjoint Operators A,B with B≥0 Such That -B≤A≤B but |A|≤B -- 7.2.17 The Failure of the Inequality |"426830A Ax,x"526930B |≤"426830A |A|x,x"526930B -- 7.2.18 On the Generalized Cauchy-Schwarz Inequality -- 7.2.19 On the Failure of Some Variants of the Generalized Cauchy-Schwarz Inequality -- 7.2.20 A Sequence of Self-Adjoint Operators (An) Such That "026B30D |An|-|A|"026B30D 0 But "026B30D An-A"026B30D 0 -- 7.2.21 The Non-weakly Continuity of A|A| -- 7.2.22 A Sequence of Operators (An) Converging Strongly to A, but (|An|) Does Not Converge Strongly to |A| -- 7.2.23 An Invertible A=U|A| with U|A|≠|A|U, UA≠AU, and A|A|≠|A|A -- 7.2.24 Left or Right Invertible Operators Do Not Enjoy a (``Unitary'') Polar Decomposition -- 7.2.25 A Normal Operator Whose Polar Decomposition Is Not Unique -- 7.2.26 On a Result of the Uniqueness of the Polar Decomposition By Ichinose-Iwashita -- 7.2.27 An Operator A Expressed as A=V|A| with A3=0 but V3≠0 -- 7.2.28 An Invertible Operator A Expressed as A=U|A| with A3=I but U3≠I -- Answers. 8 Spectrum. |
| Record Nr. | UNINA-9910568266203321 |
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Mortad Mohammed Hichem <1978->
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Dilations, Completely Positive Maps and Geometry / / by B.V. Rajarama Bhat, Tirthankar Bhattacharyya
| Dilations, Completely Positive Maps and Geometry / / by B.V. Rajarama Bhat, Tirthankar Bhattacharyya |
| Autore | Bhat B. V. Rajarama |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (236 pages) |
| Disciplina | 515.724 |
| Altri autori (Persone) | BhattacharyyaTirthankar |
| Collana | Texts and Readings in Mathematics |
| Soggetto topico |
Operator theory
Functional analysis Geometry Operator Theory Functional Analysis Geometry.6 Geometria Anàlisi funcional Teoria d'operadors |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-9983-52-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Dilation for One Operator -- C*-Algebras and Completely Positive Maps -- Dilation Theory in Two Variables - The Bidisc -- Dilation Theory in Several Variables - the Euclidean Ball -- The Euclidean Ball - The Drury Arveson Space -- Dilation Theory in Several Variables - The Symmetrized Bidisc -- An Abstract Dilation Theory. |
| Record Nr. | UNINA-9910831002203321 |
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Bhat B. V. Rajarama
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Soggetto topico
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Teoria d'operadors
(35)
- Operator theory (30)
- Functional analysis (8)
- Anàlisi funcional (7)
- Anàlisi harmònica (5)