Description
Book SynopsisThis 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 representation
Table of ContentsPreface
Background
Spaces with Indefinite Metric
J-Symmetric Operator Algebras and Representations on Krein Spaces
Non-Degenerate J-Symmetric Operator Algebras on (Pi)(kappa)-Spaces
J-Symmetric Operator Algebras on (Pi)1-Spaces
Representations of *-Algebras and Groups on (Pi)(kappa)-Spaces
Derivations of C*-Algebras Implemented by Skew-Symmetric Operators
Bibliography
Index
