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Operator Algebras in Dynamical Systems

Operator Algebras in Dynamical Systems

Paperback

Series: Encyclopedia of Mathematics and Its Applications, Book 41

AlgebraGeneral ScienceProbability & Statistics

ISBN10: 0521060214
ISBN13: 9780521060219
Publisher: Cambridge University Press
Published: Feb 4 2008
Pages: 232
Weight: 0.73
Height: 0.49 Width: 6.14 Depth: 9.21
Language: English
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 considerable contributions. 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 C*-theory. The presentation 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, the author 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.

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