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Spectral Theory of Operators on Hilbert Spaces, by Carlos S. Kubrusly
PDF Download Spectral Theory of Operators on Hilbert Spaces, by Carlos S. Kubrusly
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This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated.
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 also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field.
- Sales Rank: #2432637 in Books
- Brand: Brand: Birkhäuser
- Published on: 2012-06-01
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .50" w x 6.14" l, 1.03 pounds
- Binding: Hardcover
- 197 pages
- Used Book in Good Condition
Review
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)
“The book under review is intended to offer to graduate students in mathematics, as well as to those studying statistics, engineering, physics and economics, an introductory text for a first course in spectral theory. … The book is well and clearly written and a large amount of information about the spectrum of linear operators is exhibited within, including several relatively new results. It may be used both as a reference book and also as a textbook … .” (F.-H. Vasilescu, Mathematical Reviews, January, 2013)
From the Back Cover
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.
About the Author
Carlos Kubrusly was born in Rio de Janeiro in November 1947. He received his Ph.D. from the University of Warwick in 1976, held postdoctoral visiting research positions at the Universities of Warwick and Bonn, and has been a faculty member of Catholic University of Rio de Janeiro since 1972, where he became a full professor in 1988. Professor Kubrusly has published over 100 scientific articles in international journals and proceedings of international conferences. He has participated in approximately 40 scientific conferences, all with paper presentation, including plenary sections at the Toulouse IFAC Symposium in 1982 and at the Newport Beach SOTA Conference in 1998, and has also been a member of program committees of several international conferences.
Professor Kubrusly was the editor-in-chief of the journal Computational and Applied Mathematics (published by Birkhäuser from 1992 to 1998), and coeditor of the book Semigroups of Operators: Theory and Applications (Optimization Software, Los Angeles, 2002). He is the author of five books: "An Introduction to Models and Decompositions in Operator Theory", "Elements of Operator Theory", and "Hilbert Space Operators", all published by Birkhäuser in 1997, 2001, and 2003, respectively; "Measure Theory" by Academic Press in 2007; and recently, "The Elements of Operator Theory" (2nd enlarged and updated edition of "Elements of Operator Theory") published by Birkhäuser in 2011.
Most helpful customer reviews
1 of 1 people found the following review helpful.
A great book about Spectral Theory
By E. Zanni
This book mainly concern is to investigate the spectrum of operators (i.e., continuous linear transformations) on Hilbert Spaces. Unbounded operators and results on Banach space are not the focus here. It introduces classical topics such as C*-Algebra, Functional Calculus and Fredholm Theory. Futhermore, Kubrusly made a brilliant exposition of the Spectral Theorem, one the cornerstone theorems on Operator Theory on Hilbert Spaces.
1 of 1 people found the following review helpful.
Great book
By J. Garcia
Great book for studying spectral Theory! Concise and written in a friendly, thus very rigorous manner. Excellent for students who have some background in functional analysis.
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