Item description for Functional Analysis: Spectral Theory (Birkhäuser Advanced Texts / Basler Lehrbücher) by V.S. Sunder...
In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutative C*-algebras. A discussion of representations of C*-algebras follows, and the final section of this chapter is devoted to the Hahn-Hellinger classification of separable representations of commutative C*-algebras. After this detour into operator algebras, the fourth chapter reverts to more standard operator theory in Hilbert space, dwelling on topics such as the spectral theorem for normal operators, the polar decomposition theorem, and the Fredholm theory for compact operators. A brief introduction to the theory of unbounded operators on Hilbert space is given in the fifth and final chapter. There is a voluminous appendix whose purpose is to fill in possible gaps in the reader's background in various areas such as linear algebra, topology, set theory and measure theory. The book is interspersed with many exercises, and hints are provided for the solutions to the more challenging of these.
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Est. Packaging Dimensions: Length: 9.3" Width: 6.1" Height: 0.8" Weight: 1.1 lbs.
Release Date Oct 1, 1998
Publisher Birkhäuser Basel
ISBN 3764358920 ISBN13 9783764358921
Reviews - What do customers think about Functional Analysis: Spectral Theory (Birkhäuser Advanced Texts / Basler Lehrbücher)?
Simply the Best! Aug 29, 1999
There are many good functional analysis textbooks from Dunford's Linear Operators, Yoshida's Functional Analysis (those classical ones) to the latest ones by Hirsch and Sunders, I have to say Sunders' is the best in the modern treatise of the subjects. I also like his appendix for the review of topology which is also elegantly written. A good textbook is written by an understanding and experienced educators who knows exactly what the students need and how to convey them efficiently (easy to learn) and effectively (so the students won't get fructrated easily). The author connected the subjects in a music-like fashion. I am particularly fond of the flow of the book which is mmmm... Mozart style. It is great not only for the math students, but also for research physicists and practicing engineers. I enjoy this book so much that I bought a second copy for my office shelf.