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Publisher:

World Scientific

Publication Date:

2006

Number of Pages:

136

Format:

Paperback

Price:

28.00

ISBN:

9812566864

Category:

Textbook

[Reviewed by , on ]

Kenneth A. Ross

10/31/2006

This is a well-written student-friendly basic introduction to functional analysis and Hilbert space, culminating in the spectral theorem for self-adjoint linear operators on separable Hilbert space. The detailed proofs are easy to read, and the exercises are reasonable. Occasionally the presentation is too slick. The author avoids weak and strong topologies, even in Hilbert space, and this makes for a cumbersome unintuitive proof that every weakly convergent sequence in a Hilbert space is bounded.

My one complaint is that the author introduces the *L ^{p}*-spaces on

Kenneth A. Ross (ross@math.uoregon.edu) taught at the University of Oregon from 1965 to 2000. He was President of the MAA during 1995-1996. Before that he served as AMS Associate Secretary, MAA Secretary, and MAA Associate Secretary. His research area of interest was commutative harmonic analysis, especially where it has a probabilistic flavor. He is the author of the book Elementary Analysis: The Theory of Calculus (1980, now in 14th printing), co-author of Discrete Mathematics (with Charles R.B. Wright, 2003, fifth edition), and, as Ken Ross, the author of A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans (2004).

- Basic Elements of Metric Topology
- New Types of Function Spaces
- Theory of Hilbert Spaces
- Operators on Hilbert Spaces
- Spectral Theory
- Exercises and Applications

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