Geometry Of Normed Linear Spaces
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Geometry Of Linear 2 Normed Spaces
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Author : Raymond W. Freese
language : en
Publisher: Nova Publishers
Release Date : 2001
Geometry Of Linear 2 Normed Spaces written by Raymond W. Freese and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Geometry Of Normed Linear Spaces
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Author : Robert Gardner Bartle
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Geometry Of Normed Linear Spaces written by Robert Gardner Bartle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
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.
Geometry Of Normed Linear Spaces
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Author : R. G. Birtle
language : en
Publisher:
Release Date : 1986
Geometry Of Normed Linear Spaces written by R. G. Birtle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
The Geometry Of Metric And Linear Spaces
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Author : L. M. Kelly
language : en
Publisher: Springer
Release Date : 2006-11-14
The Geometry Of Metric And Linear Spaces written by L. M. Kelly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Geometry Of Banach Spaces Selected Topics
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Author : J. Diestel
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1975-09
Geometry Of Banach Spaces Selected Topics written by J. Diestel and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-09 with Mathematics categories.
Geometric Properties Of Banach Spaces And Nonlinear Iterations
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Author : Charles Chidume
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-27
Geometric Properties Of Banach Spaces And Nonlinear Iterations written by Charles Chidume and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-27 with Mathematics categories.
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.
Norm Derivatives And Characterizations Of Inner Product Spaces
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Author : Claudi Alsina
language : en
Publisher: World Scientific
Release Date : 2010
Norm Derivatives And Characterizations Of Inner Product Spaces written by Claudi Alsina and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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).
Introduction To Banach Spaces And Their Geometry
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Author :
language : en
Publisher: Elsevier
Release Date : 2011-10-10
Introduction To Banach Spaces And Their Geometry written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-10 with Mathematics categories.
Introduction to Banach Spaces and their Geometry
Geometric Functional Analysis And Its Applications
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Author : R. B. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Functional Analysis And Its Applications written by R. B. Holmes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Normed Linear Spaces
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Author : Mahlon M. Day
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Normed Linear Spaces written by Mahlon M. Day and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.