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Berezin Number Inequalities via Convex Functions
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Berezin Number Inequalities via Convex Functions
Berezin Number Inequalities via Convex Functions
Journal Article

Berezin Number Inequalities via Convex Functions

2022
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Overview
The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗(Ω) over some set Ω with the reproducing kernel kξ is defined by A ˜ ( ξ ) = 〈 A k ξ ‖ k ξ ‖ , k ξ ‖ k ξ ‖ 〉 , ξ ∈ Ω . The Berezin number of an operator A is defined by ber ( A ) : = sup ξ ∈ Ω | A ˜ ( ξ ) | . We study some problems of operator theory by using this bounded function Ã, including treatments of inner product inequalities via convex functions for the Berezin numbers of some operators. We also establish some inequalities involving of the Berezin inequalities.
Publisher
University of Nis, Faculty of Sciences and Mathematics

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