This is a short course on Banach space theory with special emphasis
on certain aspects of the classical theory. In particular, the
course focuses on three major topics: the elementary theory of
Schauder bases, an introduction to Lp spaces, and an introduction
to C(K) spaces. While these topics can be traced back to Banach
himself, our primary interest is in the postwar renaissance of
Banach space theory brought about by James, Lindenstrauss, Mazur,
Namioka, Pelczynski, and others. Their elegant and insightful
results are useful in many contemporary research endeavors and
deserve greater publicity. By way of prerequisites, the reader will
need an elementary understanding of functional analysis and at
least a passing familiarity with abstract measure theory. An
introductory course in topology would also be helpful; however, the
text includes a brief appendix on the topology needed for the
course.
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