| A Short Course on Spectral Theory 2002 Edition Contributor(s): Arveson, William (Author) |
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ISBN: 0387953000 ISBN-13: 9780387953007 Publisher: Springer OUR PRICE: $151.99 Product Type: Hardcover - Other Formats Published: November 2001 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Medical - Mathematics | Mathematical Analysis - Mathematics | Calculus |
| Dewey: 515.722 |
| LCCN: 2001032836 |
| Series: Graduate Texts in Mathematics |
| Physical Information: 0.49" H x 6.32" W x 9.32" (0.81 lbs) 142 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This 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. |