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

Salma Aljawi, Kais Feki () and Zakaria Taki
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Salma Aljawi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Kais Feki: Department of Mathematics, College of Science and Arts, Najran University, Najran 66462, Kingdom of Saudi Arabia
Zakaria Taki: Department of Mathematics, Faculy of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh 40000, Morocco

Mathematics, 2024, vol. 12, issue 7, 1-15

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.

Keywords: operator seminorm; A -bounded operator; A -numerical radius; symmetric mean; bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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