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Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge /

By: Sergey Neshveyev, Erling StÃ¸rmer

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Hardcover | 18 July 2006

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Hardcover
308 Pages

Dimensions(cm)
24.13 x 16.51 x 2.54

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During the last 30 years there have been several attempts at extending the notion of entropy to noncommutative dynamical systems. The authors present in the book the two most successful approaches to the extensions of measure entropy and topological entropy to the noncommutative setting and analyze in detail the main models in the theory.

The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Calculus & Mathematical Analysis Differential Calculus & Equations Functional Analysis & Transforms Science Physics Mathematical Physics Reference, Information & Interdisciplinary Subjects Research & Information Information theory

Cybernetics & Systems Theory

General Theory
Classical Dynamical Systems	p. 3
Measure Entropy	p. 3
Topological Entropy	p. 9
Entropy via Partitions of Unity	p. 11
Notes	p. 14
Relative Entropy	p. 15
Relative Entropy for Matrix Algebras	p. 15
Von Neumann Entropy	p. 21
Relative Entropy for General C*-algebras	p. 26
Notes	p. 30
Dynamical Entropy	p. 33
Mutual Entropy	p. 33
Entropy of Dynamical Systems	p. 48
Type I Algebras	p. 54
Notes	p. 57
Maximality of Entropy and Commutativity	p. 61
Maximal Entropy of Subalgebras	p. 61
Independent Algebras	p. 66
Entropic K-systems	p. 69
Notes	p. 74
Dynamical Abelian Models	p. 77
Entropy via Stationary Couplings	p. 77
Zero Entropy Systems	p. 86
Notes	p. 91
Topological Entropy	p. 93
Rank of a Completely Positive Approximation	p. 93
Topological Entropy	p. 96
Notes	p. 103
Dynamics on the State Space	p. 107
Measure Entropy	p. 107
Topological Entropy	p. 110
Notes	p. 119
Crossed Products	p. 121
Crossed Products by Discrete Amenable Groups	p. 121
Generalizations	p. 125
Notes	p. 130
Variational Principle	p. 133
Pressure	p. 133
The variational principle	p. 138
KMS-states	p. 144
Notes	p. 151
Special Topics
Relative Entropy and Subfactors	p. 157
Relative Entropy	p. 157
Index of Subfactors	p. 164
Generators and Relative Entropy	p. 167
The Canonical Shift	p. 171
Shifts on Temperley-Lieb Algebras	p. 180
Notes	p. 183
Systems of Algebraic Origin	p. 185
Twisted Group C*-algebras	p. 185
Estimates of Topological Entropy	p. 187
K-systems	p. 194
Zero Entropy Systems	p. 201
Automorphisms of Noncommutative Tori	p. 206
Notes	p. 209
Binary Shifts	p. 211
The C*-algebra of a Bitstream	p. 211
Entropy of Binary Shifts	p. 217
Notes	p. 224
Bogoliubov Automorphisms	p. 227
Canonical Anticommutation Relations	p. 227
Topological Entropy	p. 229
Classical Bernoullian Subsystems	p. 233
Dynamical Entropy	p. 238
Notes	p. 248
Free Products	p. 251
Free Products of Algebras and Maps	p. 251
Free Shifts	p. 254
Free Product Automorphisms	p. 257
Notes	p. 263
Completely Positive Maps	p. 265
Operator Inequalities	p. 271
Direct Integrals	p. 275
References	p. 279
List of Symbols	p. 291
Index	p. 295
Table of Contents provided by Publisher. All Rights Reserved.

Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge /

At a Glance

Hardcover

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