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arveson w short course spectral theory 2002

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Textbook in PDF format 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. Contents Preface Spectral Theory and Banach Algebras Operators on Hilbert Space Asymptotics: Compact Perturbations and Fredholm Theory Methods and Applications Bibliography Index

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Arveson W. A Short Course on Spectral Theory 2002.pdf 4.5 MB

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arveson w short course spectral theory 2002