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Operator algebras in dynamical systems : the theory of unbounded derivations in C*-algebras /
This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitio...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1991.
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 41. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Title; Copyright; Contents; Preface; 1 Preliminaries; 1.1 Banach algebras, C*-algebras and W*-algebras; 1.2 Topologies on C*-algebras and W*-algebras; 1.3 Homomorphisms, *-isomorphisms and *-automorphisms; 1.4 Self-adjointness and positivity; 1.5 Positive linear functionals and states; 1.6 Commutative C*- and W*-algebras; 1.7 Concrete C*- and W*-algebras; 1.8 Representation theorems for C*- and W*-algebras; 1.9 Commutation theorem (von Neumann's double commutant theorem); 1.10 Kaplansky's density theorem (Bounded approximations); 1.11 Gelfand-Naimark-Segal representations
- 1.12 Factorial and pure states1.13 Theorem (the Poisson kernel for the strip); 1.14 Corollary (the analytic version); 1.15 Theorem (the perturbation expansion theorem); 1.16 Corollary (the complex version); 1.17 Theorem (convergence on geometric vectors); 1.18 Proposition (the restricted C*-system); 2 Bounded derivations; Introduction; 2.1 Introduction to derivations; 2.2 The commutation relation ab
- ba = 1; 2.3 Continuity of everywhere-defined derivations; 2.4 Quantum field-theoretic observations (some unbounded derivations); 2.5 Application to bounded derivations
- 2.7 C*-dynamical systems and ground states3 Unbounded derivations; Introduction; 3.1 Definition of derivations; 3.2 Closability of derivations; 3.3 The domain of closed *-derivations; 3.4 Generators; 3.5 Unbounded derivations in commutative C*-algebras; 3.6 Transformation groups and unbounded derivations; 4 C*-dynamicaI systems; 4.0 Introduction; 4.1 Approximately inner C*-dynamics; 4.2 Ground states; 4.3 KMS states; 4.4 Bounded perturbations; 4.8 Continuous quantum systems; 4.5 UHF algebras and normal *-derivations; 4.6 Commutative normal *-derivations in UHF algebras; 4.7 Phase transitions