IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p250-d487764.html
   My bibliography  Save this article

Geometric Characterization of Injective Banach Lattices

Author

Listed:
  • Anatoly Kusraev

    (Southern Mathematical Institute and Khetagurov North-Ossetian State University, 44 Vatutina St., Vladikavkaz 362025, Russia
    These authors contributed equally to this work.)

  • Semën Kutateladze

    (Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia
    These authors contributed equally to this work.)

Abstract

This is a continuation of the authors’ previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective Banach lattice. The study bases on the Boolean valued transfer principle for injective Banach lattices. The latter states that each such lattice serves as an interpretation of an A L -space in an appropriate Boolean valued model of set theory. External identification of the internal Boolean valued properties of the corresponding A L -spaces yields a characterization of injective Banach lattices among Banach spaces and ordered Banach spaces. We also describe the structure of the dual space and present some dual characterization of injective Banach lattices.

Suggested Citation

  • Anatoly Kusraev & Semën Kutateladze, 2021. "Geometric Characterization of Injective Banach Lattices," Mathematics, MDPI, vol. 9(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:250-:d:487764
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/250/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/250/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:9:y:2021:i:3:p:250-:d:487764. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.