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© 2011

Banach Space Theory

The Basis for Linear and Nonlinear Analysis

Benefits

  • Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory

  • Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products

  • Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more

  • Includes information about further topics and directions of research and some open problems

Textbook

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 1-52
  3. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 53-81
  4. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 83-177
  5. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 179-235
  6. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 237-289
  7. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 291-330
  8. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 331-382
  9. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 383-427
  10. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 429-463
  11. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 465-477
  12. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 479-519
  13. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 521-574
  14. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 575-616
  15. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 617-656
  16. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 657-685
  17. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 687-732
  18. Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
    Pages 733-749
  19. Back Matter
    Pages 751-820

About this book

Introduction

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

Keywords

Radon-Nikodým property functional analysis infinite-dimensional Banach space theory

Authors and affiliations

  1. 1.Mathematical Institute of the Academy ofPragueCzech Republic
  2. 2.Faculty of Electrical Engineering, Department of MathematicsCzech Technical University PrahaPrahaCzech Republic
  3. 3.Mathematical Institute of the Academy ofPragueCzech Republic
  4. 4., Departamento de Matematica AplicadaUniversidad Politecnica de ValenciaValenciaSpain
  5. 5., Department of Mathematical and StatisticUniversity of AlbertaEdmontonCanada

About the authors

All of the authors have previously published with Springer.

Bibliographic information

  • Book Title Banach Space Theory
  • Book Subtitle The Basis for Linear and Nonlinear Analysis
  • Authors Marián Fabian
    Petr Habala
    Petr Hájek
    Vicente Montesinos
    Václav Zizler
  • Series Title CMS Books in Mathematics
  • DOI https://doi.org/10.1007/978-1-4419-7515-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-7514-0
  • Softcover ISBN 978-1-4939-4114-8
  • eBook ISBN 978-1-4419-7515-7
  • Series ISSN 1613-5237
  • Edition Number 1
  • Number of Pages XIII, 820
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
    Topology
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

“The material touches all the usual introductory topics plus such areas as tensor products, smoothness and other geometric issues, optimization, structure, etc. It is as current as a book this massive and wide-ranging can be. … it is a critical addition to the library of any college that has functional analysts of any stripe on its campus. … Summing Up: Essential. Graduate students and researchers/faculty.” (D. Robbins, Choice, Vol. 48 (11), July, 2011)

“The book is well-written and is essentially self-contained. All of the standard topics (as well as many other topics) are covered and the authors have accumulated a large collection of exercises on which students can hone their skills. … an impressive book that should be welcomed by students interested in learning the basic or more advanced topics in the theory of Banach spaces and by researchers in Banach spaces or related fields.” (Barry Turett, Zentralblatt MATH, Vol. 1229, 2012)

“It is designed to lead the reader from the basic concepts and principles to several streams of current research in Banach spaces. … I found the book very readable. It is clearly written and provides accessible references to many techniques that are commonly used in contemporary research in Banach space theory. … a nice book invaluable both for learning the topic and as a reference. This is definitely a book that anyone interested in Banach space theory (or functional analysis) should have on his/her desk.” (Sophocles Mercourakis, Mathematical Reviews, Issue 2012 h)

“This book is a German-style introduction to Banach Spaces. The authors have tried to include everything that might be useful in applications in optimization, PDEs, analysis … . if you need to know what a dentable Banach space is, you can find out here … . Most importantly, the book comes with a good set of indices, which should make it a useful reference.” (Fernando Q. Gouvêa, The Mathematical Association of America, June, 2011)