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.
View full description


Graduate students and research mathematicians.


Book information

  • Published: March 1988
  • ISBN: 978-0-12-252721-0


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.

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.
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.
These volumes have been prepared with great care. The exposition is clear and thorough.

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.