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Biblioteca

MARC Lista (tabellare)
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
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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. UNINA-9910495219503321
Galewski Marek  
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
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
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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.  
Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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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  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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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  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui
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
Mortad Mohammed Hichem <1978->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Extended abstracts fall 2019 : spaces of analytic functions: approximation, interpolation, sampling / / Evgeny Abakumov [and four others], editors
Extended abstracts fall 2019 : spaces of analytic functions: approximation, interpolation, sampling / / Evgeny Abakumov [and four others], editors
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2021]
Descrizione fisica 1 online resource (223 pages)
Disciplina 515.9
Collana Trends in mathematics. Research perspectives CRM Barcelona
Soggetto topico Funcions analítiques
Anàlisi matemàtica
Teoria d'operadors
Analytic functions
Mathematical analysis
Operator theory
Soggetto genere / forma Congressos
Llibres electrònics
ISBN 3-030-74417-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466567803316
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Extended abstracts fall 2019 : spaces of analytic functions: approximation, interpolation, sampling / / Evgeny Abakumov [and four others], editors
Extended abstracts fall 2019 : spaces of analytic functions: approximation, interpolation, sampling / / Evgeny Abakumov [and four others], editors
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2021]
Descrizione fisica 1 online resource (223 pages)
Disciplina 515.9
Collana Trends in mathematics. Research perspectives CRM Barcelona
Soggetto topico Funcions analítiques
Anàlisi matemàtica
Teoria d'operadors
Analytic functions
Mathematical analysis
Operator theory
Soggetto genere / forma Congressos
Llibres electrònics
ISBN 3-030-74417-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910510548603321
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui