Synopses & Reviews
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.
Review
"This is an interesting, useful and informative work, well worth the effort required to deal with its many results." R.H. Cox, Mathematical Reviews
Review
"A useful well-written guide." The American Mathematical Monthly
Synopsis
This book is intended to be used with graduate courses in Banach space theory.
Synopsis
Applications to other areas such as harmonic analysis function theory, orthogonal series and approximation theory are also given prominence in this introduction to modern Banach space theory. The book's prerequisites are a background in functional, complex, and real analysis.
Table of Contents
1. Introduction; 2. Basic concepts of Banach space theory; 3. Selected topics.