IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-8176-8188-3_2.html
   My bibliography  Save this book chapter

Convexity and Smoothness

In: Köthe-Bochner Function Spaces

Author

Listed:
  • Pei-Kee Lin

    (University of Memphis, Department of Mathematics)

Abstract

In the first part of this chapter (Section 2.1 and 2.2), we present some basic results about various types of convexity and smoothness conditions that the norm of a Banach space may satisfy. For convexity, we consider strictly convex, uniformly convex, locally uniformly convex, fully rotund, and nearly uniformly convex spaces. Particularly, we present a proof of the Schlumprecht-Odell theorem that shows that every separable reflexive Banach space admits an equivalent 2R norm. On the smoothness, we consider smooth, Fréchet smooth, uniformly Gâteaux smooth and uniformly smooth spaces. In the second part (Section 2.3), we introduce the spreading model, and we show that a Banach space X has the weak Banach-Saks property if and only if X does not have an ℓ1-spreading model.

Suggested Citation

  • Pei-Kee Lin, 2004. "Convexity and Smoothness," Springer Books, in: Köthe-Bochner Function Spaces, chapter 0, pages 101-142, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8188-3_2
    DOI: 10.1007/978-0-8176-8188-3_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-8176-8188-3_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.