This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim 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.
This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim 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.
From the reviews:
Geometry of Banach Spaces is a quite technical field which requires a fair practice of sharp tools from every domain of analysis. ... The authors of the book under review succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly. ... the book is essentially self-contained. It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated ... . I strongly recommend to every graduate student ... . (Gilles Godefroy, Mathematical Reviews, Issue 2006 h)
This book gives a self-contained overview of the fundamental ideas and basic techniques in modern Banach space theory. ... In this book one can find a systematic and coherent account of numerous theorems and examples obtained by many remarkable mathematicians. ... It is intended for graduate students and specialists in classical functional analysis. ... I think that any mathematician who is interested in geometry of Banach spaces should ... look over this book. Undoubtedly, the book will be a useful addition to any mathematical library. (Peter Zabreiko, Zentralblatt MATH, Vol. 1094 (20), 2006)
This book provides a sequel treatise on classical and modern Banach space theory. It is mainly focused on the study of classical Lebesgue spaces Lp, sequence spaces lp, and Banach spaces of continuous functions. ... There is a comprehensive bibliography (225 items). The book is understandable and requires only a basic knowledge of functional analysis ... . It can be warmly recommended to a broad spectrum of readers - to graduate students, young researchers and also to specialists in the field. (EMS Newsletter, March, 2007)