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作者 Alfsen, Erik M. (Erik Magnus), 1930-
書名 Geometry of state spaces of operator algebras [electronic resource] / Erik M. Alfsen, Frederic W. Shultz
出版項 Boston : Birkhäuser, ©2003
國際標準書號 9781461200192 (electronic bk.)
1461200199 (electronic bk.)
book jacket
說明 1 online resource (xiii, 467 pages) : illustrations
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Mathematics: theory & applications
Mathematics (Boston, Mass.)
附註 Includes bibliographical references (p. [451]-458) and index
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Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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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. Key features include: The properties used to describe state spaces are primarily of a geometric nature, but many can also be interpreted in terms of physics. There are numerous remarks discussing these connections * A quick introduction to Jordan algebras is given; 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 * The connection with Connes' notions of orientation and homogeneity in cones is explained * Chapters conclude with notes placing the material in historical context * Prerequisites are standard graduate courses in real and complex variables, measure theory, and functional analysis * Excellent bibliography and index In the authors' previous book, "State Spaces of Operator Algebras: Basic Theory, Orientations and C*-products" (ISBN 0-8176-3890-3), the role of orientations was examined and all the prerequisites on C*- algebras and von Neumann algebras, needed for this work, were provided in detail. These requisites, as well as all relevant definitions and results with reference back to State Spaces, are summarized in an appendix, further emphasizing the self-contained nature of this work. "Geometry of State Spaces of Operator Algebras" is intended for specialists in operator algebras, as well as graduate students and
Description based on print version record
鏈接 Print version: Alfsen, Erik M. (Erik Magnus), 1930- Geometry of state spaces of operator algebras. Boston : Birkhäuser, ©2003 (DLC) 2002034257 (OCoLC)50560356
主題 Quantum logic
Axiomatic set theory
Lattice theory
Jordan algebras
Functional analysis
Axiomatic set theory. fast (OCoLC)fst00824491
Functional analysis. fast (OCoLC)fst00936061
Jordan algebras. fast (OCoLC)fst00983985
Lattice theory. fast (OCoLC)fst00993426
Quantum logic. fast (OCoLC)fst01085115
Operatoralgebra. swd
Zustandsraum. swd
Electronic books
Alt Author Shultz, Frederic W., 1945-
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