IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i12p1162-d293190.html
   My bibliography  Save this article

Characterizations of Positive Operator-Monotone Functions and Monotone Riemannian Metrics via Borel Measures

Author

Listed:
  • Pattrawut Chansangiam

    (Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • Sorin V. Sabau

    (Department of Biology, Faculty of Biological Sciences, Tokai University, 5-1-1-1 Minamisawa, Minamiku, Sapporo 005-8601, Japan)

Abstract

We show that there is a one-to-one correspondence between positive operator-monotone functions on the positive reals, monotone Riemannian metrics, and finite positive Borel measures on the unit interval. This correspondence appears as an integral representation of weighted harmonic means with respect to that measure on the unit interval. We also investigate the normalized/symmetric conditions for operator-monotone functions. These conditions turn out to characterize monotone metrics and Morozowa–Chentsov functions as well. Concrete integral representations of such functions related to well-known monotone metrics are also provided. Moreover, we use this integral representation to decompose positive operator-monotone functions. Such decomposition gives rise to a decomposition of the associated monotone metric.

Suggested Citation

  • Pattrawut Chansangiam & Sorin V. Sabau, 2019. "Characterizations of Positive Operator-Monotone Functions and Monotone Riemannian Metrics via Borel Measures," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1162-:d:293190
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/12/1162/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/12/1162/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:7:y:2019:i:12:p:1162-:d:293190. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.