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Classical Banach Spaces I and II

Sequence Spaces and Function Spaces

  • Book
  • © 1996

Overview

Authors:
  1. Joram Lindenstrauss

    1. Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

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    You can also search for this author in PubMed   Google Scholar

  2. Lior Tzafriri

    1. Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

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    You can also search for this author in PubMed   Google Scholar

  • Best overview about Banach Spaces
  • Presents results with complete proofs

Part of the book series: Classics in Mathematics (CLASSICS)

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About this book

Springer-Verlag began publishing books in higher mathematics in 1920, when the seriesGrundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added.

Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers.

Classical Banach Spaces I and II

From the reviews: “...the book is written in the best tradition of the beautiful  series in which it appears. The material it presents is hard to find in other books. For people working in the structure theory of Banach spaces it will be most valuable as a source of references and inspiration. For those who wish to learn the subject the book deserves a warm welcome too.”
Medelingen van het Wiskundig Genootschap

“…The geometry of Banach lattices is a rich, beautiful, … and rewarding subject. The proof is in the reading and perusing of the masterpiece.”
Zentrablatt für Mathematik

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Table of contents (34 chapters)

  1. Front Matter

    Pages i-xxii
    Download chapter PDF

  2. a. Existence of Bases and Examples

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 1-7

  3. b. Schauder Bases and Duality

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 7-14

  4. c. Unconditional Bases

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 15-24

  5. d. Examples of Spaces Without an Unconditional Basis

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 24-29

  6. e. Tue Approximation Property

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 29-42

  7. f. Biorthogonal Systems

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 42-47

  8. g. Schauder Decompositions

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 47-52

  9. a. Projections in c0 and IP and Characterizations of these Spaces

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 53-63

  10. b. Absolutely Summing Operators and Uniqueness of Unconditional Bases

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 63-75

  11. c. Fredholm Operators, Strictly Singular Operators and Complemented Subspaces of lp ⊕lr

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 75-84

  12. d. Subspaces of c0 and lp and the Approximation Property, Complementably Universal Spaces

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 84-95

  13. e. Banach Spaces Containing lp or c0

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 95-104

  14. f. Extension and Lifting Properties, Automorphisms of l∞, c0 and c1

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 104-112

  15. a. Properties of Symmetrie Bases, Examples and Special Block Bases

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 113-123

  16. b. Subspaces of Spaces with a Symmetrie Basis

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 123-136

  17. a. Subspaces of Orlicz Sequence Spaces which have a Symmetrie Basis

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 137-146

  18. b. Duality and Complemented Subspaces

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 147-156

  19. c. Examples of Orlicz Sequence Spaces

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 156-166

  20. d. Modular Sequence Spaces and Subspaces of lp ⊕ lr

    • Joram Lindenstrauss, Lior Tzafriri
    Pages 166-175
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Authors and Affiliations

  • Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Joram Lindenstrauss, Lior Tzafriri

Bibliographic Information

  • Book Title: Classical Banach Spaces I and II

  • Book Subtitle: Sequence Spaces and Function Spaces

  • Authors: Joram Lindenstrauss, Lior Tzafriri

  • Series Title: Classics in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-53294-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag GmbH Germany 1996

  • Softcover ISBN: 978-3-540-60628-4Published: 05 January 1996

  • eBook ISBN: 978-3-662-53294-2Published: 24 May 2022

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 1

  • Number of Pages: XVII, 433

  • Additional Information: Originally published as Vol. 92 and Vol. 97 of the Ergebnisse der Mathematik und ihre Grenzgebiete

  • Topics: Functional Analysis

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