An introduction to the classification of amenable C-algebras [[electronic resource] /] / Huaxin Lin |
Autore | Lin Huaxin <1956-> |
Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
Descrizione fisica | 1 online resource (333 p.) |
Disciplina | 512.55 |
Soggetto topico |
C*-algebras
Banach algebras |
ISBN |
1-281-95143-9
9786611951436 981-279-988-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Preface; Contents; Chapter 1 The Basics of C*-algebras; 1.1 Banach algebras; 1.2 C*-algebras; 1.3 Commutative C*-algebras; 1.4 Positive cones; 1.5 Approximate identities, hereditary C*-subalgebras and quotients; 1.6 Positive linear functionals and a Gelfand-Naimark theorem; 1.7 Von Neumann algebras; 1.8 Enveloping von Neumann algebras and the spectral theorem; 1.9 Examples of C*-algebras; 1.10 Inductive limits of C*-algebras; 1.11 Exercises; 1.12 Addenda; Chapter 2 Amenable C*-algebras and K-theory; 2.1 Completely positive linear maps and the Stinespring representation
2.2 Examples of completely positive linear maps2.3 Amenable C*-algebras; 2.4 K-theory; 2.5 Perturbations; 2.6 Examples of K-groups; 2.7 K-theory of inductive limits of C*-algebras; 2.8 Exercises; 2.9 Addenda; Chapter 3 AF-algebras and Ranks of C*-algebras; 3.1 C*-algebras of stable rank one and their K-theory; 3.2 C*-algebras of lower rank; 3.3 Order structure of K-theory; 3.4 AF-algebras; 3.5 Simple C*-algebras; 3.6 Tracial topological rank; 3.7 Simple C*-algebras with TR(A) < 1; 3.8 Exercises; 3.9 Addenda; Chapter 4 Classification of Simple AT-algebras; 4.1 Some basics about AT-algebras 4.2 Unitary groups of C*-algebras with real rank zero4.3 Simple AT-algebras with real rank zero; 4.4 Unitaries in simple C*-algebra with RR(A) = 0; 4.5 A uniqueness theorem; 4.6 Classification of simple AT-algebras; 4.7 Invariants of simple AT-algebras; 4.8 Exercises; 4.9 Addenda; Chapter 5 C*-algebra Extensions; 5.1 Multiplier algebras; 5.2 Extensions of C*-algebras; 5.3 Completely positive maps to Mn(C); 5.4 Amenable completely positive maps; 5.5 Absorbing extensions; 5.6 A stable uniqueness theorem; 5.7 K-theory and the universal coefficient theorem 5.8 Characterization of KK-theory and a universal multi-coefficient theorem5.9 Approximately trivial extensions; 5.10 Exercises; Chapter 6 Classification of Simple Amenable C*-algebras; 6.1 An existence theorem; 6.2 Simple AH-algebras; 6.3 The classification theorems; 6.4 Invariants and some isomorphism theorems; Bibliography; Index |
Record Nr. | UNINA-9910782396703321 |
Lin Huaxin <1956->
![]() |
||
Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
An introduction to the classification of amenable C-algebras [[electronic resource] /] / Huaxin Lin |
Autore | Lin Huaxin <1956-> |
Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
Descrizione fisica | 1 online resource (333 p.) |
Disciplina | 512.55 |
Soggetto topico |
C*-algebras
Banach algebras |
ISBN |
1-281-95143-9
9786611951436 981-279-988-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Preface; Contents; Chapter 1 The Basics of C*-algebras; 1.1 Banach algebras; 1.2 C*-algebras; 1.3 Commutative C*-algebras; 1.4 Positive cones; 1.5 Approximate identities, hereditary C*-subalgebras and quotients; 1.6 Positive linear functionals and a Gelfand-Naimark theorem; 1.7 Von Neumann algebras; 1.8 Enveloping von Neumann algebras and the spectral theorem; 1.9 Examples of C*-algebras; 1.10 Inductive limits of C*-algebras; 1.11 Exercises; 1.12 Addenda; Chapter 2 Amenable C*-algebras and K-theory; 2.1 Completely positive linear maps and the Stinespring representation
2.2 Examples of completely positive linear maps2.3 Amenable C*-algebras; 2.4 K-theory; 2.5 Perturbations; 2.6 Examples of K-groups; 2.7 K-theory of inductive limits of C*-algebras; 2.8 Exercises; 2.9 Addenda; Chapter 3 AF-algebras and Ranks of C*-algebras; 3.1 C*-algebras of stable rank one and their K-theory; 3.2 C*-algebras of lower rank; 3.3 Order structure of K-theory; 3.4 AF-algebras; 3.5 Simple C*-algebras; 3.6 Tracial topological rank; 3.7 Simple C*-algebras with TR(A) < 1; 3.8 Exercises; 3.9 Addenda; Chapter 4 Classification of Simple AT-algebras; 4.1 Some basics about AT-algebras 4.2 Unitary groups of C*-algebras with real rank zero4.3 Simple AT-algebras with real rank zero; 4.4 Unitaries in simple C*-algebra with RR(A) = 0; 4.5 A uniqueness theorem; 4.6 Classification of simple AT-algebras; 4.7 Invariants of simple AT-algebras; 4.8 Exercises; 4.9 Addenda; Chapter 5 C*-algebra Extensions; 5.1 Multiplier algebras; 5.2 Extensions of C*-algebras; 5.3 Completely positive maps to Mn(C); 5.4 Amenable completely positive maps; 5.5 Absorbing extensions; 5.6 A stable uniqueness theorem; 5.7 K-theory and the universal coefficient theorem 5.8 Characterization of KK-theory and a universal multi-coefficient theorem5.9 Approximately trivial extensions; 5.10 Exercises; Chapter 6 Classification of Simple Amenable C*-algebras; 6.1 An existence theorem; 6.2 Simple AH-algebras; 6.3 The classification theorems; 6.4 Invariants and some isomorphism theorems; Bibliography; Index |
Record Nr. | UNINA-9910810899203321 |
Lin Huaxin <1956->
![]() |
||
Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Invariant means and finite representation theory of C-algebras / / Nathanial P. Brown |
Autore | Brown Nathanial P (Nathanial Patrick), <1972-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
Descrizione fisica | 1 online resource (122 p.) |
Disciplina | 512/.556 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
C*-algebras
Representations of algebras |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-0469-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Notation, definitions and useful facts""; ""Chapter 3. Amenable traces and stronger approximation properties""; ""3.1. Characterizations of amenable traces""; ""3.2. Uniform amenable traces""; ""3.3. Quasidiagonal traces""; ""3.4. Locally finite dimensional traces""; ""3.5. Miscellaneous remarks and permanence properties""; ""Chapter 4. Examples and special cases""; ""4.1. Discrete groups""; ""4.2. Nuclear and WEP C*- algebras""; ""4.3. Locally reflexive, exact and quasidiagonal C*-algebras""; ""4.4. Type I C*-algebras""
""4.5. Tracially AF C*-algebras""""Chapter 5. Finite representations""; ""5.1. Ili-factor representations of some universal C*-algebras""; ""5.2. Elliott's intertwining argument for IIi-factors""; ""5.3. Hi-factor representations of Popa Algebras""; ""Chapter 6. Applications and connections with other areas""; ""6.1. Elliott's classification program""; ""6.2. Counterexamples to questions of Lin and Popa""; ""6.3. Connes' embedding problem""; ""6.4. Amenable traces and numerical analysis""; ""6.5. Amenable traces and obstructions in K-homology"" ""6.6. Stable finiteness versus quasidiagonality""""6.7. Questions""; ""Bibliography"" |
Record Nr. | UNINA-9910480876803321 |
Brown Nathanial P (Nathanial Patrick), <1972->
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Invariant means and finite representation theory of C-algebras / / Nathanial P. Brown |
Autore | Brown Nathanial P (Nathanial Patrick), <1972-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
Descrizione fisica | 1 online resource (122 p.) |
Disciplina | 512/.556 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
C*-algebras
Representations of algebras |
ISBN | 1-4704-0469-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Notation, definitions and useful facts""; ""Chapter 3. Amenable traces and stronger approximation properties""; ""3.1. Characterizations of amenable traces""; ""3.2. Uniform amenable traces""; ""3.3. Quasidiagonal traces""; ""3.4. Locally finite dimensional traces""; ""3.5. Miscellaneous remarks and permanence properties""; ""Chapter 4. Examples and special cases""; ""4.1. Discrete groups""; ""4.2. Nuclear and WEP C*- algebras""; ""4.3. Locally reflexive, exact and quasidiagonal C*-algebras""; ""4.4. Type I C*-algebras""
""4.5. Tracially AF C*-algebras""""Chapter 5. Finite representations""; ""5.1. Ili-factor representations of some universal C*-algebras""; ""5.2. Elliott's intertwining argument for IIi-factors""; ""5.3. Hi-factor representations of Popa Algebras""; ""Chapter 6. Applications and connections with other areas""; ""6.1. Elliott's classification program""; ""6.2. Counterexamples to questions of Lin and Popa""; ""6.3. Connes' embedding problem""; ""6.4. Amenable traces and numerical analysis""; ""6.5. Amenable traces and obstructions in K-homology"" ""6.6. Stable finiteness versus quasidiagonality""""6.7. Questions""; ""Bibliography"" |
Record Nr. | UNINA-9910788743203321 |
Brown Nathanial P (Nathanial Patrick), <1972->
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Invariant means and finite representation theory of C-algebras / / Nathanial P. Brown |
Autore | Brown Nathanial P (Nathanial Patrick), <1972-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
Descrizione fisica | 1 online resource (122 p.) |
Disciplina | 512/.556 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
C*-algebras
Representations of algebras |
ISBN | 1-4704-0469-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Notation, definitions and useful facts""; ""Chapter 3. Amenable traces and stronger approximation properties""; ""3.1. Characterizations of amenable traces""; ""3.2. Uniform amenable traces""; ""3.3. Quasidiagonal traces""; ""3.4. Locally finite dimensional traces""; ""3.5. Miscellaneous remarks and permanence properties""; ""Chapter 4. Examples and special cases""; ""4.1. Discrete groups""; ""4.2. Nuclear and WEP C*- algebras""; ""4.3. Locally reflexive, exact and quasidiagonal C*-algebras""; ""4.4. Type I C*-algebras""
""4.5. Tracially AF C*-algebras""""Chapter 5. Finite representations""; ""5.1. Ili-factor representations of some universal C*-algebras""; ""5.2. Elliott's intertwining argument for IIi-factors""; ""5.3. Hi-factor representations of Popa Algebras""; ""Chapter 6. Applications and connections with other areas""; ""6.1. Elliott's classification program""; ""6.2. Counterexamples to questions of Lin and Popa""; ""6.3. Connes' embedding problem""; ""6.4. Amenable traces and numerical analysis""; ""6.5. Amenable traces and obstructions in K-homology"" ""6.6. Stable finiteness versus quasidiagonality""""6.7. Questions""; ""Bibliography"" |
Record Nr. | UNINA-9910828649103321 |
Brown Nathanial P (Nathanial Patrick), <1972->
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
An invitation to C*-algebras / W. Arveson |
Autore | Arveson, William |
Pubbl/distr/stampa | Berlin : Springer, 1976 |
Descrizione fisica | x, 106 p. ; 24 cm. |
Soggetto topico |
C*-algebras
Hilbert space Representations of algebras |
Classificazione |
510.46
512'.55 QA326 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991001036869707536 |
Arveson, William
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Berlin : Springer, 1976 | ||
![]() | ||
Lo trovi qui: Univ. del Salento | ||
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An invitation to C*-algebras / William Arveson |
Autore | Arveson, William |
Pubbl/distr/stampa | New York : Springer-Verlag, 1976 |
Descrizione fisica | x, 106 p. ; 24 cm |
Disciplina | 512.724 |
Collana | Graduate texts in mathematics, 0072-5285 ; 39 |
Soggetto topico |
C*-algebras
Hilbert space Representations of algebras |
ISBN | 0387901760 |
Classificazione |
AMS 46L05
AMS 47C10 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991001043699707536 |
Arveson, William
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New York : Springer-Verlag, 1976 | ||
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Lo trovi qui: Univ. del Salento | ||
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Iterated function systems and permutation representations of the Cuntz algebra / / Ola Bratteli, Palle E.T. Jorgensen |
Autore | Bratteli Ola |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1999] |
Descrizione fisica | 1 online resource (106 p.) |
Disciplina |
510 s
512/.55 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
C*-algebras
Fourier analysis Representations of groups Hilbert space |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-0252-1 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Contents""; ""List of Figures""; ""Chapter 1. Introduction""; ""Chapter 2. Permutative representations of O[sub(N)]""; ""Chapter 3. Monomial representations and integers modulo N""; ""Chapter 4. Cycles of irreducible O[sub(N)] representations and their atoms of UHF[sub(N)] representations""; ""Chapter 5. Relations of finite type and sub-Cuntz states""; ""Chapter 6. The shift representation""; ""Chapter 7. The universal permutative multiplicity-free representation""; ""Chapter 8. Some specific examples of the cycle and atom structure: The mod N case""; ""8.1. The case N = 2"" |
Record Nr. | UNINA-9910480499603321 |
Bratteli Ola
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [1999] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Iterated function systems and permutation representations of the Cuntz algebra / / Ola Bratteli, Palle E.T. Jorgensen |
Autore | Bratteli Ola |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1999] |
Descrizione fisica | 1 online resource (106 p.) |
Disciplina |
510 s
512/.55 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
C*-algebras
Fourier analysis Representations of groups Hilbert space |
ISBN | 1-4704-0252-1 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Contents""; ""List of Figures""; ""Chapter 1. Introduction""; ""Chapter 2. Permutative representations of O[sub(N)]""; ""Chapter 3. Monomial representations and integers modulo N""; ""Chapter 4. Cycles of irreducible O[sub(N)] representations and their atoms of UHF[sub(N)] representations""; ""Chapter 5. Relations of finite type and sub-Cuntz states""; ""Chapter 6. The shift representation""; ""Chapter 7. The universal permutative multiplicity-free representation""; ""Chapter 8. Some specific examples of the cycle and atom structure: The mod N case""; ""8.1. The case N = 2"" |
Record Nr. | UNINA-9910788737603321 |
Bratteli Ola
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [1999] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Iterated function systems and permutation representations of the Cuntz algebra / / Ola Bratteli, Palle E.T. Jorgensen |
Autore | Bratteli Ola |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1999] |
Descrizione fisica | 1 online resource (106 p.) |
Disciplina |
510 s
512/.55 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
C*-algebras
Fourier analysis Representations of groups Hilbert space |
ISBN | 1-4704-0252-1 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Contents""; ""List of Figures""; ""Chapter 1. Introduction""; ""Chapter 2. Permutative representations of O[sub(N)]""; ""Chapter 3. Monomial representations and integers modulo N""; ""Chapter 4. Cycles of irreducible O[sub(N)] representations and their atoms of UHF[sub(N)] representations""; ""Chapter 5. Relations of finite type and sub-Cuntz states""; ""Chapter 6. The shift representation""; ""Chapter 7. The universal permutative multiplicity-free representation""; ""Chapter 8. Some specific examples of the cycle and atom structure: The mod N case""; ""8.1. The case N = 2"" |
Record Nr. | UNINA-9910808069303321 |
Bratteli Ola
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [1999] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
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