A Short Course on Spectral Theory

William Arveson (auth.)9780387953007, 0387953000, 9780387215181

This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative k-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here. The book is based on a fifteen-week course which the author offered to first or second year graduate students with a foundation in measure theory and elementary functional analysis.

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Table of contents :
Front Matter….Pages i-x
Spectral Theory and Banach Algebras….Pages 1-38
Operators on Hilbert Space….Pages 39-81
Asymptotics: Compact Perturbations and Fredholm Theory….Pages 83-100
Methods and Applications….Pages 101-129
Back Matter….Pages 131-141