Open Problems in the Geometry and Analysis of Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Open Problems in the Geometry and Analysis of Banach Spaces write by Antonio J. Guirao. This book was released on 2016-07-26. Open Problems in the Geometry and Analysis of Banach Spaces available in PDF, EPUB and Kindle. 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.
Handbook of the Geometry of Banach Spaces
Handbook of the Geometry of Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of the Geometry of Banach Spaces write by . This book was released on 2001-08-15. Handbook of the Geometry of Banach Spaces available in PDF, EPUB and Kindle. 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.
Geometry of Banach Spaces and Related Fields
Geometry of Banach Spaces and Related Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry of Banach Spaces and Related Fields write by Gilles Godefroy. This book was released on 2024-03-27. Geometry of Banach Spaces and Related Fields available in PDF, EPUB and Kindle. This book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography. This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.
Geometric Properties of Banach Spaces and Nonlinear Iterations
Geometric Properties of Banach Spaces and Nonlinear Iterations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Properties of Banach Spaces and Nonlinear Iterations write by Charles Chidume. This book was released on 2009-03-27. Geometric Properties of Banach Spaces and Nonlinear Iterations available in PDF, EPUB and Kindle. 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.
Geometry and Nonlinear Analysis in Banach Spaces
Geometry and Nonlinear Analysis in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry and Nonlinear Analysis in Banach Spaces write by Kondagunta Sundaresan. This book was released on 2006-11-14. Geometry and Nonlinear Analysis in Banach Spaces available in PDF, EPUB and Kindle.
