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arXiv · 2112.10186

Inequalities involving Berezin norm and Berezin number

Pintu Bhunia·Kallol Paul·Anirban Sen
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Abstract

We obtain new inequalities involving Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space $\mathscr{H}.$ Among many inequalities obtained here, it is shown that if $A$ is a positive bounded linear operator on $\mathscr{H}$, then $\|A\|_{ber}=\textbf{ber}(A)$, where $\|A\|_{ber}$ and $\textbf{ber}(A)$ 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.

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Pintu Bhunia, Kallol Paul, Anirban Sen. 2021-12-19. Inequalities involving Berezin norm and Berezin number. https://arxiv.org/abs/2112.10186

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