Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles: Basic Representation Theory of Groups and Algebras

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J. M.G. Fell, R. S. Doran
Academic Press, Apr 15, 1988 - Mathematics - 746 pages
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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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Contents

Introduction to Volume 1 Capter I to VII
1
Chapter I Preliminaries
41
Chapter II Integration Theory and Banach Bundles
63
Chapter III Locally Compact Groups
163
Chapter IV Algebraic Representation Theory
265
Chapter V Locally Convex Representations and Banach Algebras
323
Chapter VI CAlgebras and Their Representations
377
Chapter VII The Topology of the Space of Representations
539
Appendix A The StoneWeierstrass Theorems
613
Appendix B Unbounded Operators in Hilbert Space
619
Appendix C The Existence of Continuous CrossSections of Banach Bundles
633
Bibliography
643
Name Index
721
Subject Index
725
Index of Notation
739
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