Linear Analysis and Representation Theory

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Dover Publications, 2010 - Mathematics - 688 pages
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A frequently cited scholarly text, this unified treatment constitutes an ideal reference for graduate math students and mathematicians. Its clear, accurate formulations offer a relatively self-contained resource for those studying locally compact groups, Lie groups and algebras, harmonic analysis, and the representation of groups.
An introductory chapter on algebras and Banach algebras is followed by a summary of linear functional analysis and examinations of spectral theorem, stable subspaces, and von Neumann algebras. Subsequent chapters explore elementary representation theory in Hilbert space; topological groups, invariant measures, convolutions, and representations; the basic theory of induced representations; and fundamentals of the theory of representations of compact groups. The final chapters offer a concise introduction to the theory of Lie algebras, Lie groups, and transform groups.

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JA Chapter I Algebras and Banach Algebras Algebras and Norms
The Group of Units and the Quasigroup
The Maximal Ideal Space

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