Elements Of Geometry Of Balls In Banach Spaces

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Elements Of Geometry Of Balls In Banach Spaces

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Author : Kazimierz Goebel
language : en
Publisher: Oxford University Press
Release Date : 2018-09-06

Elements Of Geometry Of Balls In Banach Spaces written by Kazimierz Goebel and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-06 with Mathematics categories.

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.

Handbook Of The Geometry Of Banach Spaces

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language : en
Publisher: Elsevier
Release Date : 2001-08-15

Handbook Of The Geometry Of Banach Spaces 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 2001-08-15 with Mathematics categories.

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

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Author : Gilles Godefroy
language : en
Publisher: American Mathematical Society
Release Date : 2024-03-27

Geometry Of Banach Spaces And Related Fields written by Gilles Godefroy and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-27 with Mathematics categories.

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.

Physical Applications Of Homogeneous Balls

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Author : Yaakov Friedman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-08

Physical Applications Of Homogeneous Balls written by Yaakov Friedman 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 2013-01-08 with Mathematics categories.

One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework. This text introduces precisely such a broad mathematical model, one that gives a clear geometric expression of the symmetry of physical laws and is entirely determined by that symmetry. The first three chapters discuss the occurrence of bounded symmetric domains (BSDs) or homogeneous balls and their algebraic structure in physics. The book further provides a discussion of how to obtain a triple algebraic structure associated to an arbitrary BSD; the relation between the geometry of the domain and the algebraic structure is explored as well. The last chapter contains a classification of BSDs revealing the connection between the classical and the exceptional domains.

Nonlinear Semigroups Fixed Points And Geometry Of Domains In Banach Spaces

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Author : Simeon Reich
language : en
Publisher: World Scientific
Release Date : 2005-07-12

Nonlinear Semigroups Fixed Points And Geometry Of Domains In Banach Spaces written by Simeon Reich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-12 with Mathematics categories.

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments./a

The Volume Of Convex Bodies And Banach Space Geometry

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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 1999-05-27

The Volume Of Convex Bodies And Banach Space Geometry written by Gilles Pisier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-27 with Mathematics categories.

A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.

Spear Operators Between Banach Spaces

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Author : Vladimir Kadets
language : en
Publisher: Springer
Release Date : 2018-04-16

Spear Operators Between Banach Spaces written by Vladimir Kadets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-16 with Mathematics categories.

This monograph is devoted to the study of spear operators, that is, bounded linear operators G between Banach spaces X and Y satisfying that for every other bounded linear operator T:X → Y there exists a modulus-one scalar ω such that ǁ G+ωTǁ = 1 + ǁTǁ. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on L1. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.

Banach Space Theory And Its Applications

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Author : A. Pietsch
language : en
Publisher: Springer
Release Date : 2006-11-15

Banach Space Theory And Its Applications written by A. Pietsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

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