Books : Representations on Krein Spaces [Hot] and Derivations of C*-Algebras (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)
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Binding: HardcoverDewey Decimal Number: 516
EAN: 9780582231573
ISBN: 0582231574
Label: Chapman & Hall/CRC
Manufacturer: Chapman & Hall/CRC
Number Of Items: 1
Number Of Pages: 616
Publication Date: October 03, 1997
Publisher: Chapman & Hall/CRC
Sales Rank: 6949612
Studio: Chapman & Hall/CRC
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This text provides a comprehensive treatment of representations on indefinite metric spaces, and their applications to the theory of *-derivations of C*-algebras.The book consists of two parts. The first studies the geometry of indefinite metric spaces (Krein and (Pi)(kappa)-spaces) and describes the theory of J-symmetric operator algebras and representations of *-algebras and groups on these spaces in a systematic form. For representations on (Pi)(kappa)-spaces, many significant new results are obtained; this establishes a possible approach to the general theory of representations.In the second part, different techniques of the theory of J-symmetric representations on Krein spaces are applied to the theory of *-derivations of C*-algebras implemented by skew-symmetric and dissipative operators. Various results are obtained, which establish a link between the deficiency indices of skew-symmetric operators implementing *-derivations of C*-algebras and dimensions of representations of these algebras. The problem of isomorphism of skew-symmetric operators is also touched upon.Numerous properties of the domains of *-derivations are investigated. These domains constitute an important subclass of differentiable Banach *-algebras, that is dense *-subalgebras of C*-algebras with properties in many respects similar to the properties of algebras of differentiable functions. The Weyl operator commutation relations are examined in the general context of *-derivations of C*-algebras. Powersà and ArvesonÃs indices of one-parameter semigroups of *-endomorphisms of the algebra B are considered, and various notions of the index of a *-derivation are introduced and studied.Application of the theory of J-symmetric representations on Krein spaces to the theory of *-derivations of C*-algebras is a new research area of growing interest and there are many exciting advances to be made in this field. The book covers a fairly large and complex body of material, and will serve as a stimulus to further research activity in this area.
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- I wonder if I could understand........I teach Math high school students at home. Secretly, being a schoolgirl, I was bored with my calculating capacity. In many Math subjects, I was interested in infinitude only. Though nobody explained me about it, A. Einstein's book was my best friend. Because he said, "Math is only a tool." above all he was humorous and romantic. I wonder if I could understand Algebras by V.S. Edward Kissin........ Keep the idea to myself, for we make sincere efforts to........
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