Operator algebras in dynamical systems: the theory of unbounded derivations in C-algebras
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1991
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| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 219 S. |
| ISBN: | 0521400961 9780521400961 9780521060219 |
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Record in the Search Index
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| adam_text | Titel: Operator algebras in dynamical systems
Autor: Sakai, Shôichirô
Jahr: 1991
CONTENTS Preface ix 1 Preliminaries 1 1.1 Banach algebras, C*-algebras and W*-algebras 1 1.2 Topologies on C*-algebras and W*-algebras 2 1.3 Homomorphisms, *-isomorphisms and *-automorphisms 2 1.4 Self-adjointness and positivity 2 1.5 Positive linear functionals and states 2 1.6 Commutative C*- and W*-algebras 3 1.7 Concrete C*- and W*-algebras 3 1.8 Representation theorems for C*- and W*-algebras 5 1.9 Commutation theorem (von Neumann’s double commutant 5 theorem) 1.10 Kaplansky’s density theorem (Bounded approximations) 5 1.11 Gelfand-Naimark-Segal representations 5 1.12 Factorial and pure states 6 1.13 Theorem (the Poisson kernel for the strip) 7 1.14 Corollary (the analytic version) 7 1.15 Theorem (the perturbation expansion theorem) 7 1.16 Corollary (the complex version) 9 1.17 Theorem (convergence on geometric vectors) 11 1.18 Proposition (the restricted C*-system) 14 2 Bounded derivations 16 2.1 Introduction to derivations 17 2.2 The commutation relation ab — ba- 1 17 2.3 Continuity of everywhere-defined derivations 22 2.4 Quantum field-theoretic observations (some unbounded derivations) 24 2.5 Application to bounded derivations 34 2.6 Uniformly continuous dynamical systems 41 2.7 C*-dynamical systems and ground states 48 vii
Contents viii 3 Unbounded derivations 55 3.1 Definition of derivations 56 3.2 Closability of derivations 58 3.3 The domain of closed ‘-derivations 65 3.4 Generators 72 3.5 Unbounded derivations in commutative C*-algebras 79 3.6 Transformation groups and unbounded derivations 94 4 C*-dynamical systems 101 4.1 Approximately inner C*-dynamics 101 4.2 Ground states 107 4.3 KMS states 114 4.4 Bounded perturbations 130 4.5 UHF algebras and normal ‘-derivations 155 4.6 Commutative normal ‘-derivations in UHF algebras 153 4.7 Phase transitions ¡75 4.8 Continuous quantum systems jg^ References 207 Index 217
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| author | Sakai, Shôichirô |
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| discipline | Mathematik |
| edition | 1. publ. |
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| language | English |
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| physical | XI, 219 S. |
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| spelling | Sakai, Shôichirô Verfasser aut Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras Shôichirô Sakai 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1991 XI, 219 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 41 Algèbre Banasch Jussieu Algèbre opérateur Jussieu Analyse combinatoire Analyse harmonique Analyse harmonique Jussieu Analyse harmonique ram C* - algèbres ram C*-algebra's gtt C*-algèbre Jussieu Dynamique différentiable Dynamische systemen gtt Operatoren gtt Opérateurs, Théorie des Opérateurs, théorie des ram Systèmes dynamiques différentiables ram W*-algèbre Jussieu C*-algebras Differentiable dynamical systems Harmonic analysis Operator theory Operatoralgebra (DE-588)4129366-6 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s DE-604 Harmonische Analyse (DE-588)4023453-8 s C-Stern-Algebra (DE-588)4136693-1 s Differenzierbares dynamisches System (DE-588)4137931-7 s Encyclopedia of mathematics and its applications 41 (DE-604)BV000903719 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002830291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sakai, Shôichirô Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras Encyclopedia of mathematics and its applications Algèbre Banasch Jussieu Algèbre opérateur Jussieu Analyse combinatoire Analyse harmonique Analyse harmonique Jussieu Analyse harmonique ram C* - algèbres ram C*-algebra's gtt C*-algèbre Jussieu Dynamique différentiable Dynamische systemen gtt Operatoren gtt Opérateurs, Théorie des Opérateurs, théorie des ram Systèmes dynamiques différentiables ram W*-algèbre Jussieu C*-algebras Differentiable dynamical systems Harmonic analysis Operator theory Operatoralgebra (DE-588)4129366-6 gnd C-Stern-Algebra (DE-588)4136693-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4129366-6 (DE-588)4136693-1 (DE-588)4023453-8 (DE-588)4137931-7 |
| title | Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras |
| title_auth | Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras |
| title_exact_search | Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras |
| title_full | Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras Shôichirô Sakai |
| title_fullStr | Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras Shôichirô Sakai |
| title_full_unstemmed | Operator algebras in dynamical systems the theory of unbounded derivations in C-algebras Shôichirô Sakai |
| title_short | Operator algebras in dynamical systems |
| title_sort | operator algebras in dynamical systems the theory of unbounded derivations in c algebras |
| title_sub | the theory of unbounded derivations in C-algebras |
| topic | Algèbre Banasch Jussieu Algèbre opérateur Jussieu Analyse combinatoire Analyse harmonique Analyse harmonique Jussieu Analyse harmonique ram C* - algèbres ram C*-algebra's gtt C*-algèbre Jussieu Dynamique différentiable Dynamische systemen gtt Operatoren gtt Opérateurs, Théorie des Opérateurs, théorie des ram Systèmes dynamiques différentiables ram W*-algèbre Jussieu C*-algebras Differentiable dynamical systems Harmonic analysis Operator theory Operatoralgebra (DE-588)4129366-6 gnd C-Stern-Algebra (DE-588)4136693-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Algèbre Banasch Algèbre opérateur Analyse combinatoire Analyse harmonique C* - algèbres C*-algebra's C*-algèbre Dynamique différentiable Dynamische systemen Operatoren Opérateurs, Théorie des Opérateurs, théorie des Systèmes dynamiques différentiables W*-algèbre C*-algebras Differentiable dynamical systems Harmonic analysis Operator theory Operatoralgebra C-Stern-Algebra Harmonische Analyse Differenzierbares dynamisches System |
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