Geometry of State Spaces of Operator Algebras
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Beschreibung
This monograph presents a complete and self-contained solution to the
long-standing problem of giving a geometric description of state
spaces of C*-algebras and von Neumann algebras, and of their Jordan
algebraic analogs (JB-algebras and JBW-algebras). The material, which
previously has appeared only in research papers and required
substantial prerequisites for a reader's understanding, is made
accessible here to a broad mathematical audience. Geometry of State
Spaces of Operator Algebras is intended for specialists in operator
algebras, as well as graduate students and mathematicians in other
areas.
Gives a quick introduction to Jordan algebras; no previous knowledge is assumed and all necessary background on the subject is given A discussion of dynamical correspondences, which tie together Lie and Jordan structures, and relate the observables and the generators of time evolution in physics Chapters conclude with notes placing the material in historical context
Autor*in
Erik M. Alfsen
Themen in »Geometry of State Spaces of Operator Algebras«
Algebra applications mathematics functional analysis knot theory manifolds mathematical physics operator algebra
Stimmen zu »Geometry of State Spaces of Operator Algebras«
From the reviews:
"The two books together provide a predominantly self-contained presentation of the geometric theory of operator algebra state spaces, culminating in the classification theorem of Alfsen, Hanche–Olsen and Shultz. Until now much of this material has been accessible only in the original papers, which makes the two volumes a welcome addition to the literature. . . . The result is a clear and comprehensive account. . . . the book describes a beautiful solution to a problem dating back to the foundations of the subject."
—MATHEMATICAL REVIEWS
"Notable results…are presented in this book in a unified way, with complete and enlightening proofs and comments. The authors have done fine work for the mathematical community, providing a valuable toolkit for researchers interested in non-associative structures, self-adjoint operator algebras, or areas of functional analysis or mathematical physics where aspects related to convexity and ordered spaces appear…."
—ZENTRALBLATT MATH
"The aim of the present book is to give a complete geometric description of the state spaces of operator algebras, meaning to give axiomatic characterizations of those convex sets that are state spaces … . The book is divided into three parts. … It is aimed to specialists in operator algebras, graduate students and mathematicians working in other areas (mathematical physics, foundation of quantum mechanics).” (S. Cobzas, Mathematica, Vol. 46 (2), 2004)
"The authors of this monograph present a complete and self-contained solution to the long-standing problem of giving a geometric description of state spaces … . There also are an Appendix, a Bibliography containing 137 references, and an Index. The material, which previously has appeared only in research papers … is made accessible here to a broad mathematical audience. … The book under review is intended for specialists in operatoralgebras, as well as graduate students and mathematicians in other areas.” (Radu Iordanescu, Revue Roumaine de Mathématiques Pures et Appliquées, Vol. XLIX (3), 2004)
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