A Short Course on Banach Space Theory [Hardcover]

This is a short course on Banach space theory applicable to many contemporary research arenas.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. The book is intended for use as in an advanced topics course or seminar, or for independent study. It offers a gentler introduction than can be found in the existing literature, even including elementary exercises. In addition, the text 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. The book is intended for use as in an advanced topics course or seminar, or for independent study. It offers a gentler introduction than can be found in the existing literature, even including elementary exercises. In addition, the text includes references to expository articles and suggestions for further reading.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.Preface; 1. Classical Banach spaces; 2. Preliminaries; 3. Bases in Banach spaces; 4. Bases inl-