A Short Course on Banach Space Theory (London Mathematical Society Student Texts, Series Number 64)

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. "This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular the course concentrates on three major topics. The elementary theory of Schauder bases an introduction to L[subscript p] spaces, and an introduction to C(K) spaces." "The book is intended for use an in an advanced topics course or seminar or for independent study. This volume offers a gentler introduction than can be found in the existing literature and even includes elementary exercises. In addition, the text presents references to expository articles and suggestions for further reading."--BOOK JACKET 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. This is a short course on classical Banach space theory. It 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

this Is A Short Course On Banach Space Theory Applicable To Many Contemporary Research Arenas.