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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.
|
| Colección: | Encyclopedia of mathematics and its applications ;
v. 41. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 020 | |a 9781107088238 |q (electronic bk.) | ||
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| 029 | 1 | |a DEBBG |b BV043128670 | |
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| 035 | |a (OCoLC)715185597 | ||
| 050 | 4 | |a QA326 |b .S26 1991eb | |
| 072 | 7 | |a MAT |x 002040 |2 bisacsh | |
| 082 | 0 | 4 | |a 512/.55 |2 22 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Sakai, Shôichirô, |d 1928- | |
| 245 | 1 | 0 | |a Operator algebras in dynamical systems : |b the theory of unbounded derivations in C*-algebras / |c Shôichirô Sakai. |
| 260 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1991. | ||
| 300 | |a 1 online resource (xi, 219 pages). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v v. 41 | |
| 504 | |a Includes bibliographical references (pages 207-216) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a C*-algebras. | |
| 650 | 0 | |a Differentiable dynamical systems. | |
| 650 | 0 | |a Harmonic analysis. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 2 | |a Fourier Analysis | |
| 650 | 6 | |a C*-algèbres. | |
| 650 | 6 | |a Dynamique différentiable. | |
| 650 | 6 | |a Analyse harmonique. | |
| 650 | 6 | |a Théorie des opérateurs. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a C*-algebras. |2 fast |0 (OCoLC)fst00843285 | |
| 650 | 7 | |a Differentiable dynamical systems. |2 fast |0 (OCoLC)fst00893426 | |
| 650 | 7 | |a Harmonic analysis. |2 fast |0 (OCoLC)fst00951490 | |
| 650 | 7 | |a Operator theory. |2 fast |0 (OCoLC)fst01046419 | |
| 650 | 7 | |a C-Stern-Algebra |2 gnd | |
| 650 | 7 | |a Differenzierbares dynamisches System |2 gnd | |
| 650 | 7 | |a Operatoralgebra |2 gnd | |
| 650 | 7 | |a Harmonische Analyse |2 gnd | |
| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v v. 41. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569299 |z Texto completo |
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