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Operator algebras and quantum statistical mechanics. 1. \(C^*\)- and \(W^*\)-algebras, symmetry groups, decomposition of states. 2nd ed. (English) Zbl 0905.46046

Texts and Monographs in Physics. New York, NY: Springer. xiv, 505 p. (1987).
{The first edition (1979) was reviewed in detail in Zbl 0421.46048. There is a Russian translation of Volume I [Moscow (1982; Zbl 0523.46043)], and Volume II has been reviewed [Springer, New York (1981; Zbl 0463.46052)].}
Preface to the second edition: “The second edition of this book differs from the original in three respects. First, we have eliminated a large number of typographical errors. Second, we have corrected a small number of mathematical oversights. Third, we have rewritten several subsections in order to incorporate new or improved results. The principal changes occur in Chapters 3 and 4.”
“Section 3.1.2 now contains a more comprehensive discussion of dissipative operators and analytic elements. Additions and changes have also been made in Sections 3.1.3, 3.1.4, and 3.1.5. Further improvements occur in Section 3.2.4. In Chapter 4 the only substantial changes are to Sections 4.2.1 and 4.2.2. At the time of writing the first edition it was an open question whether maximal orthogonal probability measures on the state space of a \(C^*\)-algebra were automatically maximal among all the probability measures on the space. This question was resolved positively in 1979, and the rewritten sections now incorporate the result.”
“All these changes are nevertheless revisionary in nature and do not change the scope of the original edition. In particular, we have resisted the temptation to describe the developments of the last seven years in the theory of derivations, and dissipations, associated with \(C^*\)-dynamical systems. The current state of this theory is summarized in the recent monograph by the first author [“Derivations, dissipations, and group actions on \(C^*\)-algebras”, Lect. Notes Math. 1229 (1986; Zbl 0607.46035)].”
The second edition of Volume II has been published by Springer in 1997.

MSC:

46L60 Applications of selfadjoint operator algebras to physics
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
46L55 Noncommutative dynamical systems
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
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