A Short Course on Banach Space Theory

N.L. Carothers - Collection London Mathematical Society Student Texts

196 pages, parution le 02/03/2005

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Résumé

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.

L'auteur - N.L. Carothers

N. L. Carothers : Bowling Green State University, Ohio

Sommaire

Classical Banach spaces
Preliminaries
Bases in Banach spaces
Bases in Banach spaces II
Bases in Banach spaces III
Special properties of C0, L1, and l
Bases and duality
Lp spaces
Lp spaces II
Lp spaces III
Convexity
C(K) Spaces
Weak compactness in L1
The Dunford-Pettis property
C(K) Spaces II
C(K) Spaces III
Topology review

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	N.L. Carothers
Collection	London Mathematical Society Student Texts
Parution	02/03/2005
Nb. de pages	196
Format	15 x 22,5
Couverture	Broché
Poids	275g
Intérieur	Noir et Blanc
EAN13	9780521603720
ISBN13	978-0-521-60372-0