A Short Course on Spectral Theory: 209 (Graduate Texts in Mathematics, 209)

Arveson, William

ISBN 10: 0387953000 / ISBN 13: 9780387953007

Published by Springer, 2001

About this Item

The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged.

Seller Inventory # GOR009493349

Bibliographic Details

• Title: A Short Course on Spectral Theory: 209 (Graduate Texts in Mathematics, 209)
• Publisher: Springer
• Publication Date: 2001
• Language: English
• ISBN 10: 0387953000
• ISBN 13: 9780387953007
• Binding: Hardback
• Condition: Very Good
• Weight: 367 grams

About this title

Synopsis

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.

From the Back Cover

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.