Inequalities of generalized Euclidean Berezin number

Abstract

In this paper, we present several Berezin number inequalities involving extensions of Euclidean Berezin number for n operators. Among other inequalities for $(T_{1},\ldots,T_{n})\in{\mathbb B}(\mathcal H)$ we show that
\begin{align*}
\textbf{ber}_{\textbf{p}}^{p}(T_{1},\ldots,T_{n})\leq\frac{1}{2^{p}}\textbf{ber}\left(\sum_{i=1}^{n}(|T_{i}|+
|T_{i}^{*}|)^{p}\right),
\end{align*}
where $p>1$.