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C^{*}-Algebras.
This volume contains the proceedings of an AMS Special Session held at the Joint Mathematics Meetings in San Antonio in January 1993 to celebrate the first fifty years of C^*-algebra theory. The book contains carefully written expository and research articles by leaders in the field. Also included i...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1994.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; Preface; On the imbedding of normed rings into the ring of operators in Hilbert space; Notes on the Gelfand-Neumark theorem; C*-algebras and quantization; Quantization and C*-algebras; Some quantizations and reflections inspired by the Gelfand-Naimark theorem; The role of C*-algebras in infinite dimensional numerical linear algebra; Projections in C*-algebras; C*-algebras and Mackey's theory of group representations; Transformation group C*-algebras: A selective survey; Algebraic topology and C*-algebras; 1. The initial early contacts; 2. Kasparov's bivariant homology theory.
- 3. Digression: A missed opportunity in topology4. K-Theory enters operator theory; 5. Torsion and Universal Coefficient Theorems; 6. The Kasparov Spectral Sequence; 7. The Limits of Algebraic Topology; 8. Applications to algebraic topology; Twenty-five years in the theory of type III von Neumann algebras; Classifying space for proper actions and K-theory of group C*-algebras; 0. Introduction; 1. Proper Actions; 2. Examples of EG; 3. Equivariant K-Homology; 4. Lie Groups; 5. Cosheaf Homology; 6. p-adic Groups; 7. Discrete Groups; 8. An Equivariant Novikov Conjecture.
- 9. The Conjecture with CoefficientsA1. Infinite Join Construction of EG; A2. Axioms for EG; A3. What Does BG Classify?; Odd index theorems and operator algebras; Index theory without symbols; 0. Introduction; 1. Alexander-Spanier Character; 1.1 Alexander-Spanier homology; 1.2 Support filtration and associated K-groups; 1.3 Antisymmetrized trace homomorphism; 1.4 Alexander-Spanier character: even case; 1.5 Suspended Chern character; 1.6 Alexander-Spanier character: odd case; 2. The Character Class; 2.1 Finite-dimensional K-class; 2.2 The character class: even case.
- 2.3 The character class: odd case2.4 The character class: unbounded picture; 3. The Homological Chern Character; 3.1 Pseudo-differential K-cycles; 3.2 Lipschitz K-cycles; A survey of exponential rank; 0. Introduction; 1. Definitions and motivation for exponential rank; 2. Some historical remarks; 3. Algebras of matrix valued functions and stable C*-algebras; 4. Real rank zero, weak (FU), and weak (FN); 5. Simple C*-algebras with real rank greater than zero; 6. Exponential length and multiplier algebras; 7. Exponential rank of Banach algebras; 8. Projective length and rank; 9. Commutators.
- 10. Other factorization problems11. Real and imaginary relations between the various ranks; 12. Applications; Appendix; On the imbedding of normed rings into the ring of operators in Hilbert space.