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Author : Anonim
Publisher : Elsevier
Page : 870 pages
File Size : 40,6 Mb
Release : 2003-05-06
Category : Mathematics
ISBN : 0080533507
Handbook of the Geometry of Banach Spaces
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2024-06-10
Category : Electronic
ISBN : OCLC:944497191
Author : J. Diestel
Publisher : Springer
Page : 298 pages
File Size : 53,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540379133
Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 54,5 Mb
Release : 2001-08-15
Category : Mathematics
ISBN : 9780080532806
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.
Author : I. Cioranescu
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400921214
One service mathematics has rendered the 'Et moi ... - si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author : Anonim
Publisher : Elsevier
Page : 307 pages
File Size : 48,5 Mb
Release : 2011-10-10
Category : Mathematics
ISBN : 0080871798
Introduction to Banach Spaces and their Geometry
Author : Gilles Pisier
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 47,8 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821807101
This book surveys the considerable progress made in Banach space theory as a result of Grothendieck's fundamental paper ""Resume De la Theorie Metrique des Produits Tensoriels Topologiques"". The author examines the central question of which Banach spaces $X$ and $Y$ have the property that every bounded operator from $X$ to $Y$ factors through a Hilbert space, in particular when the operators are defined on a Banach lattice, a $C^*$-algebra or the disc algebra and $H^\infty$. He reviews the six problems posed at the end of Grothendieck's paper, which have now all been solved (except perhaps the exact value of Grothendieck's constant), and includes the various results which led to their solution. The last chapter contains the author's construction of several Banach spaces such that the injective and projective tensor products coincide; this gives a negative solution to Grothendieck's sixth problem.Although the book is aimed at mathematicians working in functional analysis, harmonic analysis and operator algebras, its detailed and self-contained treatment makes the material accessible to nonspecialists with a grounding in basic functional analysis. In fact, the author is particularly concerned to develop very recent results in the geometry of Banach spaces in a form that emphasizes how they may be applied in other fields, such as harmonic analysis and $C^*$-algebras.
Author : Kazimierz Goebel,Stanislaw Prus
Publisher : Oxford University Press
Page : 256 pages
File Size : 51,5 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 : Anonim
Publisher : Cambridge University Press
Page : 288 pages
File Size : 41,5 Mb
Release : 1990
Category : Banach spaces
ISBN : 9780521408509
Author : Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer
Page : 169 pages
File Size : 49,5 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319335728
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.
Author : Gilles Godefroy,Mohammad Sal Moslehian,Juan Benigno Seoane-Sepúlveda
Publisher : American Mathematical Society
Page : 358 pages
File Size : 43,8 Mb
Release : 2024-03-27
Category : Mathematics
ISBN : 9781470475703
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.
Author : Albrecht Pietsch,Jörg Wenzel
Publisher : Cambridge University Press
Page : 565 pages
File Size : 54,9 Mb
Release : 1998-09-10
Category : Mathematics
ISBN : 9780521624626
This book describes the interplay between orthonormal expansions and Banach space geometry.
Author : Joseph Diestel
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 1975
Category : Banach spaces
ISBN : OCLC:260117840
Author : Gerard Meurant
Publisher : Elsevier
Page : 765 pages
File Size : 52,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080934402
Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.
Author : Fernando Albiac,Nigel J. Kalton
Publisher : Springer
Page : 508 pages
File Size : 43,6 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9783319315577
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews