This distinctive introduction to one of the most far–reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader’s mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including:
- Weak topologies and applications
- Operators on Banach spaces
- Bases in Banach spaces
- Sequences, series, and geometry in Banach spaces
Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well–organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.
Basic Definitions and Examples.
Basic Principles with Applications.
Weak Topologies and Applications.
Operators on Banach Spaces.
Bases in Banach Spaces.
Sequences, Series, and a Little Geometry in Banach Spaces.
"...a useful book which helps the student to understand Banach space theory." (Mathematical Reviews, 2003a)