| 期刊全稱 | A Short Course on Spectral Theory | | 影響因子2023 | William Arveson | | 視頻video | http://file.papertrans.cn/143/142152/142152.mp4 | | 發(fā)行地址 | Presents basic tools of modern analysis within the context of the fundamental problem of operator theory.Includes supplementary material: | | 學(xué)科分類 | Graduate Texts in Mathematics | | 圖書封面 |  | | 影響因子 | 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 opera | | Pindex | Book 2002 |
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