A short course on Banach space theory / N.L. Carothers.

Format:

Book

Author/Creator:

Carothers, N. L., 1952- author.

Series:

London Mathematical Society student texts ; 64.

London Mathematical Society student texts ; 64

Language:

English

Subjects (All):

Banach spaces.

Physical Description:

1 online resource (xii, 184 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Series-title; Title; Copyright; Contents; Preface; Chapter 1 Classical Banach Spaces; Chapter 2 Preliminaries; Chapter 3 Bases in Banach Spaces; Chapter 4 Bases in Banach Spaces II; Chapter 5 Bases in Banach Spaces III; Chapter 6 Special Properties of...; Chapter 7 Bases and Duality; Chapter 8 Lp Spaces; Chapter 9 Lp Spaces II; Chapter 10 Lp Spaces III; Chapter 11 Convexity; Chapter 12 C(K) Spaces; Chapter 13 Weak Compactness in L1; Chapter 14 The Dunford-Pettis Property; Chapter 15 C(K) Spaces II; Chapter 16 C(K) Spaces III; Appendix Topology Review; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 173-179) and index.

ISBN:

1-107-14050-1

0-511-20650-X

0-511-08047-6

0-511-56750-2

0-511-61405-5

0-511-07971-0

OCLC:

437146061