Albiac F., Kalton N.J. Topics in Banach Space Theory

Springer Inc., 2006. — 372 p. — (Graduate Texts in Mathematics 233) — ISBN13: 978-0387-28141-4.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 Lp (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.
Fernando Albiac received his PhD in 2000 from Universidad Publica de Navarra, Spain. He is currently Visiting Assistant Professor of Mathematics at the University of Missouri,
Columbia. Nigel Kalton is Professor of Mathematics at the University of Missouri, Columbia. He has written over 200 articles with more than 82 different co-authors, and most recently, was the recipient of the 2004 Banach medal of the Polish Academy of Sciences.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 Lp-Spaces for 1 ≤ p < ∞
Factorization Theory
Absolutely Summing Operators
Perfectly Homogeneous Bases and Their Applications
p-Subspaces of Banach Spaces
Finite Representability of p-Spaces
An Introduction to Local Theory
Important Examples of Banach SpacesFundamental Notions B Elementary Hilbert Space Theory
Main Features of Finite-Dimensional Spaces
Cornerstone Theorems of Functional Analysis
Convex Sets and Extreme
The Weak Topologies
Weak Compactness of Sets and Operators