With many new concrete examples and historical notes,
Topological Vector Spaces, Second Edition provides one of the most
thorough and up-to-date treatments of the Hahn-Banach theorem. This
edition explores the theorem's connection with the axiom of choice,
discusses the uniqueness of Hahn-Banach extensions, and includes an
entirely new chapter on vector-valued Hahn-Banach theorems. It also
considers different approaches to the Banach-Stone theorem as well
as variations of the theorem.
The book covers locally convex spaces; barreled, bornological,
and webbed spaces; and reflexivity. It traces the development of
various theorems from their earliest beginnings to present day,
providing historical notes to place the results in context. The
authors also chronicle the lives of key mathematicians, including
Stefan Banach and Eduard Helly.
Suitable for both beginners and experienced researchers, this
book contains an abundance of examples, exercises of varying levels
of difficulty with many hints, and an extensive bibliography and
index.
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