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A short course on Banach space theory

✍ Scribed by N. L. Carothers

Book ID
127399853
Publisher
Cambridge University Press
Year
2004
Tongue
English
Weight
795 KB
Series
London Mathematical Society Student Texts
Category
Library
ISBN
0521603722

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Subjects

Функциональный анализ

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