Topics in Banach Space Theory

Fernando Albiac, Nigel J. Kalton - Collection Graduate Texts in Mathematics

380 pages, parution le 07/03/2006

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Résumé

Assuming only a basic knowledge of functional analysis, the book gives the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces L_p (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. The aim of this text is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems.

Written for: Graduate mathematics students, functional analysts

Sommaire

Bases and Basic Sequences
The Classical Sequence Spaces
Special Types of Bases
Banach Spaces of Continuous Functions
L1(µ)-Spaces and C(K)-Spaces
The L_p -Spaces for 1 =< p < ∞
Factorization Theory
Absolutely Summing Operators
Perfectly Homogeneous Bases and Their Applications
l_p-Subspaces of Banach Spaces
Finite Representability of l_p -Spaces
An Introduction to Local Theory
Important Examples of Banach Spaces

A Fundamental Notions
B Elementary Hilbert Space Theory
C Main Features of Finite-Dimensional Spaces
D Cornerstone Theorems of Functional Analysis
E Convex Sets and Extreme Points
F The Weak Topologies
G Weak Compactness of Sets and Operators

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Fernando Albiac, Nigel J. Kalton
Collection	Graduate Texts in Mathematics
Parution	07/03/2006
Nb. de pages	380
Format	16 x 24
Couverture	Relié
Poids	660g
Intérieur	Noir et Blanc
EAN13	9780387281414
ISBN13	978-0-387-28141-4