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.
Graduate students and research mathematicians.
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, 1st Edition
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.
Quotes and reviews
@qu: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.
@qu: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.
@qu: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.
@source:--MONATSHEFTE FUR MATHEMATIK
@qu:These volumes have been prepared with great care. The exposition is clear and thorough.
@source:--AMERICAN MATHEMATICAL MONTHLY