Functional Analysis

A powerful introduction to one of the most active areas of
theoretical and applied mathematics

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.