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An introduction to the classification of amenable C*-algebras /
The theory and applications of C*-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C*-algebras is also regarded as non-commutative topology. About a de...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Ch. 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
- ch. 2. Amenable C*-algebras and K-theory. 2.1. Completely positive linear maps and the Stinespring representation. 2.2. Examples of completely positive linear maps. 2.3. 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
- ch. 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) [symbol] 1. 3.8. Exercises. 3.9. Addenda
- ch. 4. Classification of simple AT-algebras. 4.1. Some basics about AT-algebras. 4.2. Unitary groups of C*-algebras with real rank zero. 4.3. 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
- ch. 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 theorem. 5.9. Approximately trivial extensions. 5.10. Exercises
- ch. 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.