Synopses & Reviews
Algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional. This book begins with extensive background material that covers definitions and terminology, operators in Hilbert space, and the imprimitivity theorem.
Advancing to considerations of the algebras of operators in Hilbert space, the heart of the text examines domains of representations, operators in the enveloping algebra, and spectral theory. The final section explores covariant representations and connections, with a particular focus on infinite-dimensional Lie algebras. A helpful Appendix on the integrability of Lie algebras concludes the text.
The algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional. This survey begins with extensive background material and advances to considerations of the algebras of operators in Hilbert space and covariant representations and connections. 1988 edition.
This survey of operators in Hilbert space offers extensive background material and covers domains of representation, operators in the enveloping algebra, spectral theory, covariant representation, and infinite-dimensional Lie algebras. 1988 edition.
Table of Contents
ForewordPreface to the Dover EditionPrefaceAcknowledgmentsPart I. Background Material1. Introduction and Overview2. Definitions and Terminology3. Operators in Hilbert Space4. The Imprimitivity TheoremPart II. Algebras of Operators on Hilbert Space5. Domains of Representations6. Operators in the Enveloping Algebra7. Spectral TheoryPart III. Covariant Representations and Connections8. Infinite-Dimensional Lie AlgebrasAppendix. Integrability of Lie AlgebrasBibliographyIndex