Notes in Banach Spaces
Author | : H. Elton Lacey |
Publisher | : |
Total Pages | : 456 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : |
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Author | : H. Elton Lacey |
Publisher | : |
Total Pages | : 456 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : |
Author | : Jesus M.F. Castillo |
Publisher | : Springer |
Total Pages | : 280 |
Release | : 2007-12-03 |
Genre | : Mathematics |
ISBN | : 3540695192 |
This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.
Author | : Charles Chidume |
Publisher | : Springer Science & Business Media |
Total Pages | : 337 |
Release | : 2009-03-27 |
Genre | : Mathematics |
ISBN | : 1848821891 |
The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
Author | : J. Diestel |
Publisher | : Springer |
Total Pages | : 298 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540379134 |
Author | : H.-H. Kuo |
Publisher | : Springer |
Total Pages | : 230 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540375082 |
Author | : Pandelis Dodos |
Publisher | : Springer Science & Business Media |
Total Pages | : 180 |
Release | : 2010-05-10 |
Genre | : Mathematics |
ISBN | : 3642121527 |
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
Author | : Zdzisław Opial |
Publisher | : |
Total Pages | : 146 |
Release | : 1967 |
Genre | : Banach spaces |
ISBN | : |
Author | : Petr Hajek |
Publisher | : Springer Science & Business Media |
Total Pages | : 352 |
Release | : 2007-10-04 |
Genre | : Mathematics |
ISBN | : 038768915X |
This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
Author | : Pilar Cembranos |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 1997-11-27 |
Genre | : Mathematics |
ISBN | : 9783540637455 |
"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.
Author | : Marián Fabian |
Publisher | : Springer Science & Business Media |
Total Pages | : 820 |
Release | : 2011-02-04 |
Genre | : Mathematics |
ISBN | : 1441975152 |
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.