The Resource Topics in Banach space theory, Fernando Albiac, Nigel J. Kalton, (electronic book)
Topics in Banach space theory, Fernando Albiac, Nigel J. Kalton, (electronic book)
Resource Information
The item Topics in Banach space theory, Fernando Albiac, Nigel J. Kalton, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Topics in Banach space theory, Fernando Albiac, Nigel J. Kalton, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 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 selfcontained 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 bookĺŒsucceeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendlyĺŒ It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical commentsĺŒ 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 bookĺŒ" ĺlGilles Godefroy, Mathematical Reviews
 Language
 eng
 Edition
 Second edition.
 Extent
 1 online resource (xx, 508 pages)
 Contents

 1. Bases and Basic Sequences
 2. The Classical Sequence Spaces
 3. Special Types of Bases
 4. Banach Spaces of Continuous Functions
 5. L_{1}(\mu )Spaces and \mathcal C(K)Spaces
 6. The Spaces L_{p} for 1\le p<\infty
 7. Factorization Theory
 8. Absolutely Summing Operators
 9. Perfectly Homogeneous Bases and Their Applications
 10. Greedytype Bases
 11. \ell _pSubspaces of Banach Spaces
 12. Finite Representability of \ell _pSpaces
 13. An Introduction to Local Theory
 14. Nonlinear Geometry of Banach Spaces
 15. Important Examples of Banach Spaces
 Appendix A Normed Spaces and Operators
 Appendix B Elementary Hilbert Space Theory
 Appendix C Duality in L_{p}(\mu ): H\"older's inequality related results
 Appendix D Main Features of FiniteDimensional Spaces
 Appendix E Cornerstone Theorems of Functional Analysis
 Appendix F Convex Sets and Extreme Points
 Appendix G The Weak Topologies
 Appendix H Weak Compactness of Sets and Operators
 Appendix I Basic probability in use
 Appendix J Generalities on Ultraproducts
 Appendix K The Bochner Integral abridged
 List of Symbols
 References
 Index
 Isbn
 9783319315577
 Label
 Topics in Banach space theory
 Title
 Topics in Banach space theory
 Statement of responsibility
 Fernando Albiac, Nigel J. Kalton
 Language
 eng
 Summary
 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 selfcontained 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 bookĺŒsucceeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendlyĺŒ It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical commentsĺŒ 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 bookĺŒ" ĺlGilles Godefroy, Mathematical Reviews
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Albiac, Fernando
 Dewey number
 515/.732
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA322.2
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1946
 http://library.link/vocab/relatedWorkOrContributorName
 Kalton, Nigel J.
 Series statement
 Graduate texts in mathematics
 Series volume
 233
 http://library.link/vocab/subjectName
 Banach spaces
 Label
 Topics in Banach space theory, Fernando Albiac, Nigel J. Kalton, (electronic book)
 Antecedent source
 file reproduced from an electronic resource
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 black and white
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Bases and Basic Sequences  2. The Classical Sequence Spaces  3. Special Types of Bases  4. Banach Spaces of Continuous Functions  5. L_{1}(\mu )Spaces and \mathcal C(K)Spaces  6. The Spaces L_{p} for 1\le p<\infty  7. Factorization Theory  8. Absolutely Summing Operators  9. Perfectly Homogeneous Bases and Their Applications  10. Greedytype Bases  11. \ell _pSubspaces of Banach Spaces  12. Finite Representability of \ell _pSpaces  13. An Introduction to Local Theory  14. Nonlinear Geometry of Banach Spaces  15. Important Examples of Banach Spaces  Appendix A Normed Spaces and Operators  Appendix B Elementary Hilbert Space Theory  Appendix C Duality in L_{p}(\mu ): H\"older's inequality related results  Appendix D Main Features of FiniteDimensional Spaces  Appendix E Cornerstone Theorems of Functional Analysis  Appendix F Convex Sets and Extreme Points  Appendix G The Weak Topologies  Appendix H Weak Compactness of Sets and Operators  Appendix I Basic probability in use  Appendix J Generalities on Ultraproducts  Appendix K The Bochner Integral abridged  List of Symbols  References  Index
 Control code
 SPR953970037
 Dimensions
 unknown
 Edition
 Second edition.
 Extent
 1 online resource (xx, 508 pages)
 File format
 one file format
 Form of item
 online
 Isbn
 9783319315577
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319315577
 Other physical details
 illustrations.
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 Label
 Topics in Banach space theory, Fernando Albiac, Nigel J. Kalton, (electronic book)
 Antecedent source
 file reproduced from an electronic resource
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 black and white
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Bases and Basic Sequences  2. The Classical Sequence Spaces  3. Special Types of Bases  4. Banach Spaces of Continuous Functions  5. L_{1}(\mu )Spaces and \mathcal C(K)Spaces  6. The Spaces L_{p} for 1\le p<\infty  7. Factorization Theory  8. Absolutely Summing Operators  9. Perfectly Homogeneous Bases and Their Applications  10. Greedytype Bases  11. \ell _pSubspaces of Banach Spaces  12. Finite Representability of \ell _pSpaces  13. An Introduction to Local Theory  14. Nonlinear Geometry of Banach Spaces  15. Important Examples of Banach Spaces  Appendix A Normed Spaces and Operators  Appendix B Elementary Hilbert Space Theory  Appendix C Duality in L_{p}(\mu ): H\"older's inequality related results  Appendix D Main Features of FiniteDimensional Spaces  Appendix E Cornerstone Theorems of Functional Analysis  Appendix F Convex Sets and Extreme Points  Appendix G The Weak Topologies  Appendix H Weak Compactness of Sets and Operators  Appendix I Basic probability in use  Appendix J Generalities on Ultraproducts  Appendix K The Bochner Integral abridged  List of Symbols  References  Index
 Control code
 SPR953970037
 Dimensions
 unknown
 Edition
 Second edition.
 Extent
 1 online resource (xx, 508 pages)
 File format
 one file format
 Form of item
 online
 Isbn
 9783319315577
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319315577
 Other physical details
 illustrations.
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
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