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. Powers?and Arveson疄 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 b...
此叢書 Monographs & Surveys in Pure & Applied Math 書目
Canonical Problems in Scattering and Potential Theory Part 1: Canonical Structures in Potential Theory
Samuel Beckett Comment C"est How It Is And / et L"image: A Critical-Genetic Edition Une Edition Critic-Genetique
America"s Trade Follies
America"s Trade Follies
Developing Children"s Behaviour in the Classroom: A Practical Guide For Teachers And Students
Developing Children"s Behaviour in the Classroom: A Practical Guide For Teachers And Students
Representations on Krein Spaces [Hot] and Derivations of C*-Algebras
The Architect"s Eye
Reader"s Guide to American History
Progress in Self Psychology, V. 13: Conversations in Self Psychology
Major Short Stories of D.H. Lawrence: A Handbook
Fifty Years of the Research and theory of R.s. Lazarus: An Analysis of Historical and Perennial Issues
