Tsirelson S Space

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Tsirelson's Space

Peter G. Casazza,Thaddeus J. Shura
Tsirelson s Space Book PDF

Author : Peter G. Casazza,Thaddeus J. Shura
Publisher : Springer
Page : 212 pages
File Size : 53,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540460695

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Tsirelson's Space by Peter G. Casazza,Thaddeus J. Shura Pdf

This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).

Tsirelson's Space

Peter G. Casazza,Thaddeus J. Shura
Tsirelson s Space Book PDF

Author : Peter G. Casazza,Thaddeus J. Shura
Publisher : Springer
Page : 206 pages
File Size : 40,7 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 366217040X

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Tsirelson's Space by Peter G. Casazza,Thaddeus J. Shura Pdf

This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).

Handbook of the Geometry of Banach Spaces

Anonim
Handbook of the Geometry of Banach Spaces Book PDF

Author : Anonim
Publisher : Elsevier
Page : 873 pages
File Size : 52,6 Mb
Release : 2003-05-06
Category : Mathematics
ISBN : 9780080533506

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Handbook of the Geometry of Banach Spaces by Anonim Pdf

Handbook of the Geometry of Banach Spaces

Handbook of the Geometry of Banach Spaces

William B. Johnson,Joram Lindenstrauss
Handbook of the Geometry of Banach Spaces Book PDF

Author : William B. Johnson,Joram Lindenstrauss
Publisher : Elsevier
Page : 880 pages
File Size : 51,7 Mb
Release : 2001
Category : Banach spaces
ISBN : 0444513051

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Handbook of the Geometry of Banach Spaces by William B. Johnson,Joram Lindenstrauss Pdf

The Handbook presents an overview of most aspects of modern Banach 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 Banach space 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.

Ramsey Methods in Analysis

Spiros A. Argyros,Stevo Todorcevic
Ramsey Methods in Analysis Book PDF

Author : Spiros A. Argyros,Stevo Todorcevic
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 47,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373603

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Ramsey Methods in Analysis by Spiros A. Argyros,Stevo Todorcevic Pdf

This book contains two sets of notes prepared for the Advanced Course on R- sey Methods in Analysis given at the Centre de Recerca Matem` atica in January 2004, as part of its year-long research programme on Set Theory and its Appli- tions. The common goal of the two sets of notes is to help young mathematicians enter a very active area of research lying on the borderline between analysis and combinatorics. The solution of the distortion problem for the Hilbert space, the unconditional basic sequence problem for Banach spaces, and the Banach ho- geneous space problem are samples of the most important recent advances in this area, and our two sets of notes will give some account of this. But our main goal was to try to expose the general principles and methods that lie hidden behind and are most likely useful for further developments. The goal of the ?rst set of notes is to describe a general method of building norms with desired properties, a method that is clearly relevant when testing any sort of intuition about the in?nite-dimensional geometry of Banach spaces. The goal of the second set of notes is to expose Ramsey-theoretic methods relevant for describing the rough structure present in this sort of geometry. We would like to thank the coordinator of the Advanced Course, Joan Ba- ria, and the director of the CRM, Manuel Castellet, for giving us this challenging but rewarding opportunity. Part A SaturatedandConditional StructuresinBanachSpaces SpirosA.

Smooth Analysis in Banach Spaces

Petr Hájek,Michal Johanis
Smooth Analysis in Banach Spaces Book PDF

Author : Petr Hájek,Michal Johanis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 589 pages
File Size : 42,8 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110391992

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Smooth Analysis in Banach Spaces by Petr Hájek,Michal Johanis Pdf

This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.

Renormings in Banach Spaces

Antonio José Guirao,Vicente Montesinos,Václav Zizler
Renormings in Banach Spaces Book PDF

Author : Antonio José Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer Nature
Page : 621 pages
File Size : 53,5 Mb
Release : 2022-08-23
Category : Mathematics
ISBN : 9783031086557

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Renormings in Banach Spaces by Antonio José Guirao,Vicente Montesinos,Václav Zizler Pdf

This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.

Open Problems in the Geometry and Analysis of Banach Spaces

Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Open Problems in the Geometry and Analysis of Banach Spaces Book PDF

Author : Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer
Page : 169 pages
File Size : 44,9 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319335728

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Open Problems in the Geometry and Analysis of Banach Spaces by Antonio J. Guirao,Vicente Montesinos,Václav Zizler Pdf

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.

Computer Aided Proofs in Analysis

Kenneth R. Meyer,Dieter S. Schmidt
Computer Aided Proofs in Analysis Book PDF

Author : Kenneth R. Meyer,Dieter S. Schmidt
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461390923

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Computer Aided Proofs in Analysis by Kenneth R. Meyer,Dieter S. Schmidt Pdf

This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.

Köthe-Bochner Function Spaces

Pei-Kee Lin
K the Bochner Function Spaces Book PDF

Author : Pei-Kee Lin
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 47,8 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681883

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Köthe-Bochner Function Spaces by Pei-Kee Lin Pdf

This monograph is devoted to the study of Köthe–Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here, giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided, and the theory of Köthe–Bochner spaces is rigorously developed, with a particular focus on open problems. Extensive historical information, references, and questions for further study are included; instructive examples and many exercises are incorporated throughout. Both expansive and precise, this book’s unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

Analysis and Logic

C. Ward Henson
Analysis and Logic Book PDF

Author : C. Ward Henson
Publisher : Cambridge University Press
Page : 286 pages
File Size : 49,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0521648610

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Analysis and Logic by C. Ward Henson Pdf

This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.

Trends in Banach Spaces and Operator Theory

Anna Kamińska
Trends in Banach Spaces and Operator Theory Book PDF

Author : Anna Kamińska
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 54,8 Mb
Release : 2003
Category : Banach spaces
ISBN : 9780821832349

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Trends in Banach Spaces and Operator Theory by Anna Kamińska Pdf

This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.

Topics in Banach Space Theory

Fernando Albiac,Nigel J. Kalton
Topics in Banach Space Theory Book PDF

Author : Fernando Albiac,Nigel J. Kalton
Publisher : Taylor & Francis
Page : 404 pages
File Size : 51,7 Mb
Release : 2006-01-04
Category : Mathematics
ISBN : 038728141X

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Topics in Banach Space Theory by Fernando Albiac,Nigel J. Kalton Pdf

This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide 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.

Introduction to Banach Spaces: Analysis and Probability

Daniel Li,Hervé Queffélec
Introduction to Banach Spaces Analysis and Probability Book PDF

Author : Daniel Li,Hervé Queffélec
Publisher : Cambridge University Press
Page : 463 pages
File Size : 55,8 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9781107160514

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Introduction to Banach Spaces: Analysis and Probability by Daniel Li,Hervé Queffélec Pdf

This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

Fixed Point Theory And Applications - Proceedings Of The Second International Conference

Kok Keong Tan
Fixed Point Theory And Applications Proceedings Of The Second International Conference Book PDF

Author : Kok Keong Tan
Publisher : World Scientific
Page : 394 pages
File Size : 54,6 Mb
Release : 1992-08-08
Category : Electronic
ISBN : 9789814554305

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Fixed Point Theory And Applications - Proceedings Of The Second International Conference by Kok Keong Tan Pdf

This volume contains current works of researchers from twelve different countries on fixed point theory and applications. Topics include, in part, nonexpansive mappings, multifunctions, minimax inequalities, applications to game theory and computation of fixed points. It is valuable to pure and applied mathematicians as well as computing scientists and mathematical economists.