Fundamentals of Infinite Dimensional Representation Theory: 1st Edition (Hardback) book cover

Fundamentals of Infinite Dimensional Representation Theory

1st Edition

By Raymond C. Fabec

Chapman and Hall/CRC

448 pages

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Hardback: 9781584882121
pub: 2000-06-28
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pub: 2018-10-03
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Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject.

From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.


"Fabec's book seeks to give a self-contained treatment of abstract representation theory of groups and operator algebras, assuming only basic measure theory and functional analysis; and it succeeds quite well… To sum up, the book provides, for anyone interested in abstract infinite-dimensional representation theory, an accessible source of a clear, essentially self-contained, austere and business-like treatment of a wide range of topics, including technical aspects and tools required."

-Mathematical Reviews, Issue 2001m

Table of Contents

Borel Spaces and Selection Theorems

Preliminaries of C* Algebras

Type One von Neumann Algebras

Groups and Group Actions

Induced Actions and Representations

Dual Topologies

Left Hilbert Algebras

The Fourier-Stieltjes Algebra

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Algebra / General
MATHEMATICS / Functional Analysis
SCIENCE / Mathematical Physics