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.
Borel Spaces and Selection Theorems
Preliminaries of C* Algebras
Type One von Neumann Algebras
Groups and Group Actions
Induced Actions and Representations
Left Hilbert Algebras
The Fourier-Stieltjes Algebra
"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