IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/1073589.html
   My bibliography  Save this article

Orthogonal Symmetries and Reflections in Banach Spaces

Author

Listed:
  • Ali Jaballah
  • Fathi B. Saidi

Abstract

Let be a Banach space. We introduce a concept of orthogonal symmetry and reflection in . We then establish its relation with the concept of best approximation and investigate its implication on the shape of the unit ball of the Banach space by considering sections over subspaces. The results are then applied to the space of continuous functions on a compact set . We obtain some nontrivial symmetries of the unit ball of . We also show that, under natural symmetry conditions, every odd function is orthogonal to every even function in . We conclude with some suggestions for further investigations.

Suggested Citation

  • Ali Jaballah & Fathi B. Saidi, 2017. "Orthogonal Symmetries and Reflections in Banach Spaces," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, June.
    • Handle: RePEc:hin:jjmath:1073589
    DOI: 10.1155/2017/1073589
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JMATH/2017/1073589.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JMATH/2017/1073589.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/1073589?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Claudio Asci, 2016. "Differentiation Theory over Infinite-Dimensional Banach Spaces," Journal of Mathematics, Hindawi, vol. 2016, pages 1-16, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      More about this item

      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:hin:jjmath:1073589. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.