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Author : Raymond W. Freese
Publisher : Nova Publishers
ISBN 13 : 9781590330197
Total Pages : 314 pages
Book Rating : 4.3/5 (31 download)
Download or read book Geometry of Linear 2-normed Spaces written by Raymond W. Freese and published by Nova Publishers. This book was released on 2001 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Gardner Bartle
Publisher : American Mathematical Soc.
ISBN 13 : 0821850571
Total Pages : 171 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometry of Normed Linear Spaces written by Robert Gardner Bartle and published by American Mathematical Soc.. This book was released on 1986 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: These 17 papers result from a 1983 conference held to honor Professor Mahlon Marsh Day upon his retirement from the University of Illinois. Each of the main speakers was invited to take some aspect of Day's pioneering work as a starting point: he was the first American mathematician to study normed spaces from a geometric standpoint and, for a number of years, pioneered American research on the structure of Banach spaces. The material is aimed at researchers and graduate students in functional analysis. Many of the articles are expository and are written for the reader with only a basic background in the theory of normed linear spaces.
Author : R. G. Birtle
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)
Download or read book Geometry of Normed Linear Spaces written by R. G. Birtle and published by . This book was released on 1986 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. R. Giles
Publisher : Cambridge University Press
ISBN 13 : 9780521653756
Total Pages : 298 pages
Book Rating : 4.6/5 (537 download)
Download or read book Introduction to the Analysis of Normed Linear Spaces written by J. R. Giles and published by Cambridge University Press. This book was released on 2000-03-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.
Author : L. M. Kelly
Publisher : Springer
ISBN 13 : 3540379460
Total Pages : 257 pages
Book Rating : 4.5/5 (43 download)
Download or read book The Geometry of Metric and Linear Spaces written by L. M. Kelly and published by Springer. This book was released on 2006-11-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Diestel
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geometry of Banach Spaces - Selected Topics written by J. Diestel and published by Lecture Notes in Mathematics. This book was released on 1975-09 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Charles Chidume
Publisher : Springer Science & Business Media
ISBN 13 : 1848821891
Total Pages : 337 pages
Book Rating : 4.8/5 (488 download)
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.
Author : Claudi Alsina
Publisher : World Scientific
ISBN 13 : 9814287261
Total Pages : 199 pages
Book Rating : 4.8/5 (142 download)
Download or read book Norm Derivatives and Characterizations of Inner Product Spaces written by Claudi Alsina and published by World Scientific. This book was released on 2010 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. Since the appearance of Jordanvon Neumann's classical theorem (The Parallelogram Law) in 1935, the field of characterizations of inner product spaces has received a significant amount of attention in various literature texts. Moreover, the techniques arising in the theory of functional equations have shown to be extremely useful in solving key problems in the characterizations of Banach spaces as Hilbert spaces. This book presents, in a clear and detailed style, state-of-the-art methods of characterizing inner product spaces by means of norm derivatives. It brings together results that have been scattered in various publications over the last two decades and includes more new material and techniques for solving functional equations in normed spaces. Thus the book can serve as an advanced undergraduate or graduate text as well as a resource book for researchers working in geometry of Banach (Hilbert) spaces or in the theory of functional equations (and their applications).
Author :
Publisher : Elsevier
ISBN 13 : 9780080871790
Total Pages : 307 pages
Book Rating : 4.8/5 (717 download)
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 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Banach Spaces and their Geometry
Author : Jesús Ferrer
Publisher : Springer Nature
ISBN 13 : 3031236769
Total Pages : 140 pages
Book Rating : 4.0/5 (312 download)
Download or read book Geometry of the Unit Sphere in Polynomial Spaces written by Jesús Ferrer and published by Springer Nature. This book was released on 2023-03-14 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented. The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.
Author : Kalyan Mukherjea
Publisher : Springer
ISBN 13 : 9386279347
Total Pages : 299 pages
Book Rating : 4.3/5 (862 download)
Download or read book Differential Calculas in Normed Linear Spaces written by Kalyan Mukherjea and published by Springer. This book was released on 2007-08-15 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab initio exposition of the basic results concerning the topology of metric spaces, particularly of normed linear spaces.The last chapter deals with miscellaneous applications of the Differential Calculus including an introduction to the Calculus of Variations. As a corollary to this, there is a brief discussion of geodesics in Euclidean and hyperbolic planes and non-Euclidean geometry.
Author : Ian R. Porteous
Publisher :
ISBN 13 :
Total Pages : 560 pages
Book Rating : 4.3/5 (91 download)
Download or read book Topological Geometry written by Ian R. Porteous and published by . This book was released on 1969 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mahlon M. Day
Publisher : Springer
ISBN 13 : 3662416379
Total Pages : 145 pages
Book Rating : 4.6/5 (624 download)
Download or read book Normed Linear Spaces written by Mahlon M. Day and published by Springer. This book was released on 2013-12-01 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mahlon Marsh Day
Publisher : Springer
ISBN 13 : 366225249X
Total Pages : 145 pages
Book Rating : 4.6/5 (622 download)
Download or read book Normed Linear Spaces written by Mahlon Marsh Day and published by Springer. This book was released on 2013-06-29 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a compressed introduction to the study of normed linear spaces and to that part of the theory of linear topological spaces without which the main discussion could not well proceed. Definitions of many terms which are required in passing can be found in the alphabetical index, page 134. Symbols which are used throughout all, or a significant part, of this book are indexed on page 132. Each reference to the bibliography, page 124, is made by means of the author's name, supplemented when necessary by a number in square brackets. The bibliography does not completely cover the available literature, even the most recent; each paper in it is the subject of a specific reference at some point in the text. The writer takes this opportunity to express thanks to the University of Illinois, the National Science Foundation, and the University of Washington, each of which has contributed in some degree to the cultural, financial, or physical support of the writer, and to Mr. R. R. PHELPS, who eradicated many of the errors with which the manuscript was infested.
Author : Kazimierz Goebel
Publisher : Oxford University Press
ISBN 13 : 0192562320
Total Pages : 256 pages
Book Rating : 4.1/5 (925 download)
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.
Author : W. A. Coppel
Publisher : Cambridge University Press
ISBN 13 : 9780521639705
Total Pages : 236 pages
Book Rating : 4.6/5 (397 download)
Download or read book Foundations of Convex Geometry written by W. A. Coppel and published by Cambridge University Press. This book was released on 1998-03-05 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained and thorough book on the foundations of Euclidean geometry.
Author : Antonio J. Guirao
Publisher : Springer
ISBN 13 : 3319335723
Total Pages : 169 pages
Book Rating : 4.3/5 (193 download)
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 169 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.
