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Author : Raymond W. Freese,Yeol Je Cho
Publisher : Nova Publishers
Page : 314 pages
File Size : 47,9 Mb
Release : 2001
Category : Mathematics
ISBN : 1590330196
Author : Robert Gardner Bartle
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 51,8 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821850572
Features 17 papers that resulted from a 1983 conference held to honor Professor Mahlon Marsh Day upon his retirement from the University of Illinois. This work is suitable for researchers and graduate students in functional analysis.
Author : Mahlon M. Day
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 41,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662090008
Author : R. G. Birtle
Publisher : Unknown
Page : 0 pages
File Size : 49,7 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:1103663298
Author : L. M. Kelly
Publisher : Springer
Page : 257 pages
File Size : 55,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540379461
Author : J. R. Giles
Publisher : Cambridge University Press
Page : 298 pages
File Size : 43,5 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0521653754
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 : J. Diestel,Joseph Diestel
Publisher : Lecture Notes in Mathematics
Page : 302 pages
File Size : 41,9 Mb
Release : 1975-09
Category : Mathematics
ISBN : UOM:39015049318762
Author : Charles Chidume
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 50,6 Mb
Release : 2009-03-27
Category : Mathematics
ISBN : 9781848821897
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 : Anonim
Publisher : Elsevier
Page : 307 pages
File Size : 42,5 Mb
Release : 2011-10-10
Category : Mathematics
ISBN : 0080871798
Introduction to Banach Spaces and their Geometry
Author : Claudi Alsina,Justyna Sikorska,Maria Santos Tom s
Publisher : World Scientific
Page : 199 pages
File Size : 44,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814287265
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 : Jesús Ferrer,Domingo García,Manuel Maestre,Gustavo A. Muñoz,Daniel L. Rodríguez,Juan B. Seoane
Publisher : Springer Nature
Page : 140 pages
File Size : 52,7 Mb
Release : 2023-03-14
Category : Mathematics
ISBN : 9783031236761
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
Page : 299 pages
File Size : 43,9 Mb
Release : 2007-08-15
Category : Mathematics
ISBN : 9789386279347
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 : Kazimierz Goebel,Stanislaw Prus
Publisher : Oxford University Press
Page : 256 pages
File Size : 53,9 Mb
Release : 2018-09-06
Category : Mathematics
ISBN : 9780192562326
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 : Mahlon M. Day
Publisher : Springer
Page : 145 pages
File Size : 41,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783662416372
Author : R. B. Holmes
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493696
This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.