IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i7p1199-d1628604.html
   My bibliography  Save this article

Some Bounds for the Generalized Spherical Numerical Radius of Operator Pairs with Applications

Author

Listed:
  • Najla Altwaijry

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Silvestru Sever Dragomir

    (Applied Mathematics Research Group, ISILC, Victoria University, PO Box 14428, Melbourne, VIC 8001, Australia
    Mathematical Sciences, School of Science, RMIT University, Melbourne, VIC 3001, Australia)

  • Kais Feki

    (Laboratory Physics-Mathematics and Applications (LR/13/ES-22), Faculty of Sciences of Sfax, University of Sfax, Sfax 3018, Tunisia)

  • Shigeru Furuichi

    (Department of Information Science, College of Humanities and Sciences, Nihon University, Tokyo 156-8550, Japan
    Department of Mathematics Saveetha School of Engineering, SIMATS, Thandalam, Chennai 602105, India)

Abstract

This paper investigates a generalization of the spherical numerical radius for a pair ( B , C ) of bounded linear operators on a complex Hilbert space H . The generalized spherical numerical radius is defined as w p ( B , C ) : = sup x ∈ H , ∥ x ∥ = 1 | ⟨ B x , x ⟩ | p + | ⟨ C x , x ⟩ | p 1 p , p ≥ 1 . We derive lower bounds for w p 2 ( B , C ) involving combinations of B and C , where p > 1 . Additionally, we establish upper bounds in terms of operator norms. Applications include the cases where ( B , C ) = ( A , A * ) , with A * denoting the adjoint of a bounded linear operator A , and ( B , C ) = ( R ( A ) , I ( A ) ) , representing the real and imaginary parts of A , respectively. We also explore applications to the so-called Davis–Wielandt p -radius for p ≥ 1 , which serves as a natural generalization of the classical Davis–Wielandt radius for Hilbert-space operators.

Suggested Citation

  • Najla Altwaijry & Silvestru Sever Dragomir & Kais Feki & Shigeru Furuichi, 2025. "Some Bounds for the Generalized Spherical Numerical Radius of Operator Pairs with Applications," Mathematics, MDPI, vol. 13(7), pages 1-27, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1199-:d:1628604
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/7/1199/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/7/1199/
    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:13:y:2025:i:7:p:1199-:d:1628604. 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.