Operator inequalities in reproducing kernel Hilbert spaces

Year 2022, Volume: 71 Issue: 1, 204 - 211, 30.03.2022

Ulas Yamanci

https://doi.org/10.31801/cfsuasmas.926981

Abstract

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number $ber(A)$ for some self-adjoint operators $A$ on ${H}(\Omega )$.  Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ for any positive operator $A$ on ${H}(\Omega )$.

Keywords

Mulholland type inequality, Berezin number, positive operator, reproducing kernel Hilbert space, Berezin symbol

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