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Author: Petr Hajek Publisher: Springer Science & Business Media ISBN: 038768915X Category : Mathematics Languages : en Pages : 339
Book Description
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: Petr Hajek Publisher: Springer Science & Business Media ISBN: 038768915X Category : Mathematics Languages : en Pages : 339
Book Description
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: Antonio J. Guirao Publisher: Springer ISBN: 3319335723 Category : Mathematics Languages : en Pages : 169
Book Description
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.
Author: Terry J. Morrison Publisher: John Wiley & Sons ISBN: 1118031245 Category : Mathematics Languages : en Pages : 380
Book Description
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.
Author: Bor-Luh Lin Publisher: American Mathematical Soc. ISBN: 0821851578 Category : Mathematics Languages : en Pages : 201
Book Description
This volume contains the proceedings of the International Workshop on Banach Space Theory, held at the Universidad de Los Andes in Merida, Venezuela in January 1992. These refereed papers contain the newest results in Banach space theory, real or complex function spaces, and nonlinear functional analysis. There are several excellent survey papers, including ones on homogeneous Banach spaces and applications of probability inequalities, in addition to an important research paper on the distortion problem. This volume is notable for the breadth of the mathematics presented.
Author: J. Lindenstrauss Publisher: Springer Science & Business Media ISBN: 3642665578 Category : Mathematics Languages : en Pages : 202
Book Description
The appearance of Banach's book [8] in 1932 signified the beginning of a syste matic study of normed linear spaces, which have been the subject of continuous research ever since. In the sixties, and especially in the last decade, the research activity in this area grew considerably. As a result, Ban:ach space theory gained very much in depth as well as in scope: Most of its well known classical problems were solved, many interesting new directions were developed, and deep connections between Banach space theory and other areas of mathematics were established. The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces, with an emphasis on the study of the structure of the classical Banach spaces, that is C(K) and Lip.) and related spaces. We did not attempt to write a comprehensive survey of Banach space theory, or even only of the theory of classical Banach spaces, since the amount of interesting results on the subject makes such a survey practically impossible.
Author: Ivan Singer Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 688
Book Description
This monograph attempts to present the results known today on bases in Banach spaces and some unsolved problems concerning them. Although this important part of the theory of Banach spaces has been studied for more than forty years by numerous mathematicians, the existing books on functional analysis (e. g. M. M. Day [43], A. Wilansky [263], R. E. Edwards [54]) contain only a few results on bases. A survey of the theory of bases in Banach spaces, up to 1963, has been presented in the expository papers [241], [242] and [243], which contain no proofs; although in the meantime the theory has rapidly deve1oped, much of the present monograph is based on those expository papers. Independently, a useful bibliography of papers on bases, up to 1963, was compiled by B. L. Sanders [219J. Due to the vastness of the field, the monograph is divided into two volumes, ofwhich this is the first (see the tab1e of contents). Some results and problems re1ated to those treated herein have been de1iberately planned to be inc1uded in Volume 11, where they will appear in their natural framework (see [242], [243]).
Author: Petr Hajek
Author: Petr Hajek
Author: Hans Burkhardt
Author: R. E. Fullerton
Author: Fernando Albiac
Author: Antonio J. Guirao
Author: Z. Semadeni
Author: Terry J. Morrison
Author: Bor-Luh Lin
Author: J. Lindenstrauss
Author: Ivan Singer