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Other titles in the Dover Books on Physics series:
Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics / Palle E.T. Jorgensenby Palle E T Jorgensen
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.
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.
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.
Table of Contents
Preface to the Dover Edition
Part I. Background Material
1. Introduction and Overview
2. Definitions and Terminology
3. Operators in Hilbert Space
4. The Imprimitivity Theorem
Part II. Algebras of Operators on Hilbert Space
5. Domains of Representations
6. Operators in the Enveloping Algebra
7. Spectral Theory
Part III. Covariant Representations and Connections
8. Infinite-Dimensional Lie Algebras
Appendix. Integrability of Lie Algebras
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