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Representations on Krein Spaces [Hot] and Derivations of C*-Algebras : Pitman Monographs & Surveys in Pure & Applied Mathematics - Edward Kissin

Representations on Krein Spaces [Hot] and Derivations of C*-Algebras

Pitman Monographs & Surveys in Pure & Applied Mathematics

Hardcover Published: 1st January 1997
ISBN: 9780582231573
Number Of Pages: 602

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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. PowersA- and ArvesonA-s 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.

Preface
Spaces with Indefinite Metric
J-Symmetric Operator Algebras and Representations on Krein Spaces
Non-Degenerate J-Symmetric Operator Algebras on [pi][subscript k]-Spaces
J-Symmetric Operator Algebras on [pi][subscript 1]-Spaces
Representations of *-Algebras and Groups on [pi][subscript k]-Spaces
Derivations of C*-Algebras Implemented by Skew-Symmetric Operators
Bibliography
Index
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780582231573
ISBN-10: 0582231574
Series: Pitman Monographs & Surveys in Pure & Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 602
Published: 1st January 1997
Publisher: TAYLOR & FRANCIS
Country of Publication: GB
Dimensions (cm): 24.13 x 16.28  x 3.89
Weight (kg): 1.03
Edition Number: 1

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