Spectral Theory of Operators on Hilbert Spaces

Format Post in Mathematics BY Carlos S. Kubrusly

0817683275 Shared By Guest

Spectral Theory of Operators on Hilbert Spaces
Carlos S. Kubrusly
Type: eBook
Publisher: Birkhäuser
Page Count: 207
Format: pdf
Language: English
ISBN-10: 0817683275
ISBN-13: 9780817683276
From the reviews: “Kubrusly’s book … situates the spectral theorem in a very interesting broader context. … Kubrusly intends the book for a one-semester graduate course and … he closes each of his five (pretty beefy) chapters with sections titled ‘Additional Propositions.’ … I think this is a nice idea: it will make for a very solid learning experience indeed. All in all, it’s a good book.” (Michael Berg, The Mathematical Association of America, August, 2012) This work is intended to provide a concise introduction to the spectral theory of Hilbert space operators. With an emphasis on detailed proofs and recent aspects of theory, it can serve as a modern textbook for a first graduate course in the subject. The coverage of topics is thorough, exploring various intricate points and hidden features often left untreated. The book begins with a primer on Hilbert space theory, summarizing the basics required for the remainder of the book and establishing unified notation and terminology. After this, standard spectral results for (bounded linear) operators on Banach and Hilbert spaces, including the classical partition of the spectrum and spectral properties for specific classes of operators, are discussed. A study of the spectral theorem for normal operators follows, covering both the compact and the general case, and proving both versions of the theorem in full detail. This leads into an investigation of functional calculus for normal operators and Riesz functional calculus, which in turn is followed by Fredholm theory and compact perturbations of the spectrum, where a finer analysis of the spectrum is worked out. Here, further partitions involving the essential spectrum, including the Weyl and Browder spectra, are introduced. The final section of the book deals with Weyl's and Browder's theorems and provides a look at very recent results.  Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will be useful for working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to harness the applications of this theory.

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