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Product Identifiers

PublisherSpringer New York

ISBN-100387953000

ISBN-139780387953007

eBay Product ID (ePID)1942183

Product Key Features

Number of PagesX, 139 Pages

Publication NameShort Course on Spectral Theory

LanguageEnglish

Publication Year2001

SubjectFunctional Analysis, Mathematical Analysis

TypeTextbook

Subject AreaMathematics

AuthorWilliam Arveson

SeriesGraduate Texts in Mathematics Ser.

FormatHardcover

Dimensions

Item Weight30.7 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2001-032836

ReviewsFrom the reviews: MATHEMATICAL REVIEWS "This book, a product of the authora's own graduate courses on spectral theory, offers readers an expert and informed treatment of the major aspects of the spectral theory of Hilbert space operators. It is evident that a great deal of thought has gone into the choice of topics, the presentation of the results, and the design of exercises. The text is clearly written and the material is motivated in a fashion that a newcomer to the subject can readily understanda? Graduate students and experienced mathematicians alike will enjoy and benefit from a close reading of this well-written book."

Dewey Edition21

TitleLeadingA

Series Volume Number209

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal515/.7222

Table Of ContentSpectral Theory and Banach Algebras.- Operators on Hilbert Space.- Asymptotics: Compact Perturbations and Fredholm Theory.- Methods and Applications.

SynopsisThis book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to c- culate spectra of speci'c operators on in'nite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more re'ned 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 classi'cation of sim- ? ple C -algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. - ter working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert-Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the ? structure of the Toeplitz C -algebra and its connection with the topology of curves, and the index theorem for continuous symbols., 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., This book presents the basic tools of modern analysis within the context of what might be called 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 that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert-Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the ? structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols.

LC Classification NumberQA299.6-433