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A collection of seminorms linking the A -numerical radius and the operator A -seminorm

Author

Listed:
  • Salma Aljawi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
    These authors contributed equally to this work.)

  • Kais Feki

    (Department of Mathematics, College of Science and Arts, Najran University, Najran 66462, Kingdom of Saudi Arabia
    These authors contributed equally to this work.)

  • Zakaria Taki

    (Department of Mathematics, Faculy of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh 40000, Morocco
    These authors contributed equally to this work.)

Abstract

We investigate a novel operator seminorm, Q A , m λ , f , for an A -bounded operator Q , where A is a positive operator on a complex Hilbert space ( K , ⟨ · , · ⟩ ) . This seminorm is defined using a continuous increasing and bijective function f : R + ⟶ R + and an interpolational path m λ of the symmetric mean m . Specifically, Q A , m λ , f = sup f − 1 f Q y , y A m λ f Q y A : y ∈ K , y A = 1 , where f − 1 represents the reciprocal function of f , and ⟨ · , · ⟩ A and · A denote the semi-inner product and seminorm, respectively, induced by A on K . We explore various bounds and relationships associated with this new concept, establishing connections with existing literature.

Suggested Citation

  • Salma Aljawi & Kais Feki & Zakaria Taki, 2024. "A collection of seminorms linking the A -numerical radius and the operator A -seminorm," Mathematics, MDPI, vol. 12(7), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1122-:d:1372133
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