Topics in Banach Space Theory

The geometry of Banach spaces is a rich, beautiful, and rewarding subject. In this book the authors explore the isomorphic theory of Banach spaces and techniques, using the unifying viewpoint of basic sequences. Banach space theory can function as a window to such advanced concepts as harmonic analysis, and beyond into signal processing, economics and physics. The book is suitable for a semester-long graduate course and it will become a standard reference and textbook in the area.

The approach taken is the unifying viewpoint of basic sequences Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
Bases and Basic Sequences.- The Classical Sequence Spaces.- Special Types of Bases.- Banach Spaces of Continuous Functions.- L1(?)-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 Spaces.