New Inequalities and an Integral Expression for the 𠒜-Berezin Number

Salma Aljawi, Ahad Alotaibi, Cristian Conde and Kais Feki

Journal of Mathematics, 2026, vol. 2026, 1-16

Abstract: This work examines a reproducing kernel Hilbert space XF,·,· constructed on a nonempty set F. Our investigation focuses on the A-Berezin number and the A-Berezin norm, where A denotes a positive bounded linear operator acting on XF. For an A-bounded linear operator B, the A-Berezin seminorm is defined by BberA=supλ,ν∈FBu^λ,u^νA, where u^λ and u^ν are normalized reproducing kernels in XF, and f,gA=Af,g for all f,g∈XF. Similarly, the A-Berezin number is given by berAB=supλ∈FBu^λ,u^λA. The primary aim of this paper is to establish several new inequalities involving the A-Berezin seminorm and the A-Berezin number. Furthermore, we derive an explicit integral expression for the A-Berezin number and establish a necessary and sufficient condition for equality in the associated triangle inequality.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5528995

DOI: 10.1155/jom/5528995

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