IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-0255-4_11.html
   My bibliography  Save this book chapter

On Banach Algebras Generated by Two Idempotents

In: Algebraic Methods in Operator Theory

Author

Listed:
  • Ysette Weiss

Abstract

A matricial analogue of the Gel’fand map is constructed for the elements of a unital Banach algebra generated by two idempotents. For commutative unital algebras, the Gel’fand map realizes an imbedding into the algebra of all continuous functions on a well-defined set, namely the space of maximal ideals. Analogously, a semisimple algebra can be shown to be isomorphic to a subalgebra of all continuous 2 x 2 matrix-valued functions on a compact set with possible poles of order two at two points, and continuous trace. Conditions for the semisimplicity of the algebra are given, as well as a formula for the computation of the spectral radii of its elements.

Suggested Citation

  • Ysette Weiss, 1994. "On Banach Algebras Generated by Two Idempotents," Springer Books, in: Raúl E. Curto & Palle E. T. Jørgensen (ed.), Algebraic Methods in Operator Theory, pages 90-97, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0255-4_11
    DOI: 10.1007/978-1-4612-0255-4_11
    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

    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:978-1-4612-0255-4_11. 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.