On Berezin radius inequalities via Cauchy-Schwarz type inequalities:

Verda Gurdal; Hamdullah Basaran

doi:10.26637/mjm1102/002

Abstract

The Berezin transform $\widetilde{A}$ and the Berezin radius of an operator
$A$ on the reproducing kernel Hilbert space over some set $\Omega$ with the reproducing kernel $k_{\lambda}$ are defined, respectively, by \[ \widetilde{A}(\lambda)=\left\langle {A}\widehat{{k}}_{\lambda},\widehat{{k}% }_{\lambda}\right\rangle ,\ \lambda\in\Omega\text{ and }\mathrm{ber}% (A):=\sup_{\lambda\in\Omega}\left\vert \widetilde{A}{(\lambda)}\right\vert . \] We study some new inequalities by using this bounded function $\widetilde{A}, $ involving refinements of some Berezin radius inequalities for operators acting on the reproducing kernel Hilbert space.

Keywords:

Berezin symbol, Berezin radius, Cauchy-Schwarz inequality, triangle inequality, reproducing kernel

Mathematics Subject Classification:

General Mathematics

Authors Imprint References Funding Related Articles Downloads

Verda Gurdal Department of Mathematics, Suleyman Demirel University, 32260, Isparta, Turkey. https://orcid.org/0000-0001-5130-7844
Hamdullah Basaran Department of Mathematics, Suleyman Demirel University, 32260, Isparta, Turkey. https://orcid.org/0000-0002-9864-9515

Pages: 127-141
Date Published: 01-04-2023
Vol. 11 No. 02 (2023): Malaya Journal of Matematik (MJM)

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