IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-1998-9_1.html
   My bibliography  Save this book chapter

Preliminaries

In: An Introduction to Models and Decompositions in Operator Theory

Author

Listed:
  • Carlos S. Kubrusly

    (Catholic University — PUC/RJ
    National Laboratory for Scientific Computation — LNCC)

Abstract

This chapter summarizes the background material required for reading this book. Its purpose is twofold: notation and basic results. We shall try to stick to the usual notation of operator theory literature as far as possible or convenient. In particular, for a given Hubert space H, the sesquilinear form (linear in the first argument) ‹•; •›:H × H → C will stand for inner product in H. We shall not distinguish notation for norms. Thus ∥ • ∥ will denote not only the norm generated by the inner product in H (i.e. ∥x∥2 = ‹x; x› for all x ∈ H) but operator norm as well. By “basic results” we simply mean those well-known theorems that will be needed in the sequel, and only those. We shall not, in this chapter, make any attempt to prove all of them or point out a reference to each of them, but we shall refer the reader to current literature. Thus (almost) everything that is summarized here can be found, for instance, in [3, 4, 6, 7, 16, 21, 32, 62, 75, 78 and 91]. References to subsequent chapters (e.g. [17, 24, 29, 39, 40, 72 and 87]) also contain a good deal of such background material.

Suggested Citation

  • Carlos S. Kubrusly, 1997. "Preliminaries," Springer Books, in: An Introduction to Models and Decompositions in Operator Theory, chapter 0, pages 1-22, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1998-9_1
    DOI: 10.1007/978-1-4612-1998-9_1
    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:978-1-4612-1998-9_1. 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.