Download or read book Introduction to Banach Spaces and their Geometry written by and published by Elsevier. This book was released on 2011-10-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Banach Spaces and their Geometry

Download or read book Introduction to Banach Spaces and Their Geometry written by Bernard Beauzamy and published by . This book was released on 1982 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2001-08-15 with total page 1017 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Download or read book An Introduction to Banach Space Theory written by Robert E. Megginson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Download or read book Geometry of Banach Spaces Selected Topics written by J. Diestel and published by Springer. This book was released on 2006-11-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Functional Analysis written by Terry J. Morrison and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.

Download or read book Geometry of Banach Spaces Duality Mappings and Nonlinear Problems written by I. Cioranescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ... - si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Download or read book Banach Space Theory written by Marián Fabian and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Topics in Banach Space Theory written by Fernando Albiac and published by Springer. This book was released on 2016-07-19 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides 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. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving 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. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews

Download or read book Geometric Properties of Banach Spaces and Nonlinear Iterations written by Charles Chidume and published by Springer Science & Business Media. This book was released on 2009-03-27 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Functional Analysis and Infinite Dimensional Geometry written by Marian Fabian and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

Download or read book Elements of Geometry of Balls in Banach Spaces written by Kazimierz Goebel and published by Oxford University Press. This book was released on 2018-09-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects includes: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory and others. The book presents basic facts from this field.

Download or read book Factorization of Linear Operators and Geometry of Banach Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1986 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25-29, 1984"--T.p. verso.

Download or read book Geometry and Martingales in Banach Spaces written by Wojbor A. Woyczynski and published by CRC Press. This book was released on 2018-10-12 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales, and general random vectors with values in those Banach spaces. Geometric concepts such as dentability, uniform smoothness, uniform convexity, Beck convexity, etc. turn out to characterize asymptotic behavior of martingales with values in Banach spaces.

Download or read book The Volume of Convex Bodies and Banach Space Geometry written by Gilles Pisier and published by Cambridge University Press. This book was released on 1999-05-27 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.

Download or read book Geometry and Probability in Banach Spaces written by L. Schwartz and published by Springer. This book was released on 2006-11-14 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Open Problems in the Geometry and Analysis of Banach Spaces written by Antonio J. Guirao and published by Springer. This book was released on 2016-07-26 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.