Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles

Basic Representation Theory of Groups and Algebras

Edited by

  • J. Fell, University of Pennsylvania
  • R. Doran, Texas Christian University

This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
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Audience

Graduate students and research mathematicians.

 

Book information

  • Published: March 1988
  • Imprint: ACADEMIC PRESS
  • ISBN: 978-0-12-252721-0

Reviews

The authors have succeeded admirably, and these two volumes are a pleasure to read as well as being a valuable reference. [It] contains a valuable explanation of the relationship between representation theory and physics which every mathematician should be made aware of.
--MATHEMATICAL REVIEWS


There are many helpful remarks and asides throughout the text as well as extensive exercises and historical discussions at the end of each chapter. These two volumes are a valuable addition to anyone's library as well as a pleasurable avenue to representation theory.
--MATHEMATICAL REVIEW
The work is a most authoritative account of representation theory and Mackey's theory; it will no doubt become the standard work of references in thefield for years to come.
--MONATSHEFTE FUR MATHEMATIK
These volumes have been prepared with great care. The exposition is clear and thorough.
--AMERICAN MATHEMATICAL MONTHLY



Table of Contents

OF VOLUME 1: Preliminaries. Integration Theories and Banach Bundles. Locally Compact Groups. Algebraic Representation Theory. Locally Convex Representations and Banach Algebras. C*-Algebras and Their *-Representations. The Topology of the Space of *-Representations. Appendixes. Bibliography.