IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v7y1977i4p535-550.html
   My bibliography  Save this article

On the square root of a positive B(*)-valued function

Author

Listed:
  • Miamee, A. G.
  • Salehi, H.

Abstract

Let ([Omega], , [mu]) be a measure space, a separable Banach space, and * the space of all bounded conjugate linear functionals on . Let f be a weak* summable positive B(*)-valued function defined on [Omega]. The existence of a separable Hilbert space , a weakly measurable B()-valued function Q satisfying the relation Q*([omega])Q([omega]) = f([omega]) is proved. This result is used to define the Hilbert space L2,f of square integrable operator-valued functions with respect to f. It is shown that for B+(*)-valued measures, the concepts of weak*, weak, and strong countable additivity are all the same. Connections with stochastic processes are explained.

Suggested Citation

  • Miamee, A. G. & Salehi, H., 1977. "On the square root of a positive B(*)-valued function," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 535-550, December.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:4:p:535-550
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(77)90065-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:jmvana:v:7:y:1977:i:4:p:535-550. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.