A Short Course on Banach Space Theory
£40.99
Part of London Mathematical Society Student Texts
- Author: N. L. Carothers, Bowling Green State University, Ohio
- Date Published: February 2005
- availability: Available
- format: Paperback
- isbn: 9780521603720
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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.
Read more- Based on a tried-and-tested classroom approach
- The course has minimal prerequisites - accessible to anyone who has had a standard first course in graduate analysis
- The course is self-contained with numerous exercises, a preliminaries section and an appendix on topology
Reviews & endorsements
'This lively written text focuses on certain aspects of the (neo-) classical theory of Banach spaces as developed in the 1950s and 1960s and is intended as an introduction to the subject, e.g., for future Ph.D. students. … This slim book is indeed very well suited to serve as an introduction to Banach spaces. Readers who have mastered it are well prepared to study more advanced texts such as P. Wojtaszczyk's Banach Spaces for Analysts (Cambridge University Press, second edition) or research papers.' Zentralblatt MATH
See more reviews'… a painstaking attention both to detail in the mathematics and to accessibility for the reader. … You could base a good postgraduate course on it.' Bulletin of the London Mathematical Society
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×Product details
- Date Published: February 2005
- format: Paperback
- isbn: 9780521603720
- length: 198 pages
- dimensions: 229 x 151 x 11 mm
- weight: 0.3kg
- availability: Available
Table of Contents
Preface
1. Classical Banach spaces
2. Preliminaries
3. Bases in Banach spaces
4. Bases in Banach spaces II
5. Bases in Banach spaces III
6. Special properties of C0, l1, and l∞
7. Bases and duality
8. Lp spaces
9. Lp spaces II
10. Lp spaces III
11. Convexity
12. C(K) Spaces
13. Weak compactness in L1
14. The Dunford-Pettis property
15. C(K) Spaces II
16. C(K) Spaces III
A. Topology review.
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