A Short Course on Banach Space Theory

ISBN-13: 9780521603720 / Angielski / Miękka / 2004 / 198 str.

N. L. Carothers

Opis

This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas, such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use in an advanced topics course or seminar, or for independent study. It offers a more user-friendly introduction than can be found in the existing literature and includes references to expository articles and suggestions for further reading.

Recenzje

'… 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

Spis treści

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.