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 readerвЂ™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.

Functional Analysis: An Introduction to Banach Space Theory PDF

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