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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)

Label
Topics in Banach space theory
Title
Topics in Banach space theory
Statement of responsibility
Fernando Albiac, Nigel J. Kalton
Creator
Contributor
Author
Subject
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 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 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
Member of
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)
Instantiates
Publication
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. Greedy-type Bases -- 11. \ell _p-Subspaces of Banach Spaces -- 12. Finite Representability of \ell _p-Spaces -- 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 Finite-Dimensional 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
10.1007/978-3-319-31557-7
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)
Publication
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. Greedy-type Bases -- 11. \ell _p-Subspaces of Banach Spaces -- 12. Finite Representability of \ell _p-Spaces -- 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 Finite-Dimensional 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
10.1007/978-3-319-31557-7
Other physical details
illustrations.
Quality assurance targets
unknown
Reformatting quality
unknown
Specific material designation
remote

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