N. L. Carothers

Short Course on Banach Space Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 6. Dezember 2004
• Englisch
• ISBN-13: 9780511078958
• Artikelnr.: 38201311

Inhaltsangabe

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.