Operator inequalities in reproducing kernel Hilbert spaces

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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