Inequalities involving Berezin norm and Berezin number

DOI10.1007/S11785-022-01305-9arXiv2112.10186MaRDI QIDQ6386122

Pintu Bhunia, Anirban Sen, Kallol Paul

Publication date: 19 December 2021

Abstract: We obtain new inequalities involving Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space $mathscrH.$ Among many inequalities obtained here, it is shown that if $A$ is a positive bounded linear operator on $mathscrH$, then $|A{|}_{ber}=extbfber(A)$, where $|A{|}_{ber}$ and $extbfber(A)$ are the Berezin norm and Berezin number of $A$, respectively. In contrast to the numerical radius, this equality does not hold for selfadjoint operators, which highlights the necessity of studying Berezin number inequalities independently.

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12)

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