This text offers an overview of the basic theories and techniques
of functional analysis and its applications. It contains topics
such as the fixed point theory starting from Ky Fan's KKM covering
and quasi-Schwartz operators. It also includes over 200 exercises
to reinforce important concepts.;The author explores three
fundamental results on Banach spaces, together with Grothendieck's
structure theorem for compact sets in Banach spaces (including new
proofs for some standard theorems) and Helley's selection theorem.
Vector topologies and vector bornologies are examined in parallel,
and their internal and external relationships are studied. This
volume also presents recent developments on compact and weakly
compact operators and operator ideals; and discusses some
applications to the important class of Schwartz spaces.;This text
is designed for a two-term course on functional analysis for
upper-level undergraduate and graduate students in mathematics,
mathematical physics, economics and engineering. It may also be
used as a self-study guide by researchers in these disciplines.
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