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

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.
ASIN: 0387953000
VSKU: BVV.0387953000.G
Condition: Good
Author/Artist:Arveson, William
Binding: Hardcover
Note: Any images shown are stock photographs and product may differ from what is shown.
Condition Notes: The item shows wear from consistent use, but it remains in good condition and works perfectly. All pages and cover are intact including the dust cover, if applicable . Spine may show signs of wear. Pages may include limited notes and highlighting. May NOT include discs, access code or other supplemental materials.