IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-8176-4998-2_2.html
   My bibliography  Save this book chapter

Algebraic Structures

In: The Elements of Operator Theory

Author

Listed:
  • Carlos S. Kubrusly

    (Catholic University of Rio de Janeiro, Electrical Engineering Department)

Abstract

The main algebraic structure involved with the subject of this book is that of a “linear space” (or “vector space”). A linear space is a set endowed with an extra structure in addition to its set-theoretic structure (i.e., an extra structure that goes beyond the notions of inclusion, union, complement, function, and ordering, for instance). Roughly speaking, linear spaces are sets where two operations, called “addition” and “scalar multiplication”, are properly defined so that we can refer to the “sum” of two points in a linear space, as well as to the “product” of a point in it by a “scalar”. Although the reader is supposed to have already had a contact with linear algebra and, in particular, with “finite-dimensional vector spaces”, we shall proceed from the very beginning. Our approach avoids the parochially “finite-dimensional” constructions (whenever this is possible), and focuses either on general results that do not depend on the “dimensionality” of the linear space, or on abstract “infinitedimensional” linear spaces.

Suggested Citation

  • Carlos S. Kubrusly, 2011. "Algebraic Structures," Springer Books, in: The Elements of Operator Theory, chapter 2, pages 37-86, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4998-2_2
    DOI: 10.1007/978-0-8176-4998-2_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:978-0-8176-4998-2_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.