Banach Space Theory

The Basis for Linear and Nonlinear Analysis

  • Marián Fabian
  • Petr Habala
  • Petr Hájek
  • Vicente Montesinos
  • Václav Zizler
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

  • Marián Fabian
    • 1
  • Petr Habala
    • 2
  • Petr Hájek
    • 3
  • Vicente Montesinos
    • 4
  • Václav Zizler
    • 5
  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

Bibliographic information

  • 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
  • Print ISBN 978-1-4419-7514-0
  • Online ISBN 978-1-4419-7515-7
  • Series Print ISSN 1613-5237
  • About this book