Banach Spaces for Analysts (Cambridge Studies in Advanced Mathematics) Review
This book is a very readable introduction to the main techniques in functional analysis. It is worth reading, not only for a researcher in Banach space theory, but also for anyone working in mathematical analysis or anyother field of mathematics. Its content overlaps with some other recent and classical books, such as "Topics in Banach space theory" by Albiac and Kalton and "A short course in classical Banach spaces" by Carothers.
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This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis, function theory, orthogonal series, and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness, and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex, and real analysis. As the only introduction to the modern theory of Banach spaces, it will be an essential companion for professional mathematicians working in the subject, or to those interested in applying it to other areas of analysis.
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