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Berezin number and Berezin norm inequalities for operator matrices [PDF]

Linear and Multilinear Algebra, 2023
We establish new upper bounds for Berezin number and Berezin norm of operator matrices, which are refinements of the existing bounds. Among other bounds, we prove that if $A=[A_{ij}]$ is an $n\times n$ operator matrix with $A_{ij}\in\mathbb{B}(\mathcal{H})$ for $i,j=1,2\dots n$, then $\|A\|_{ber} \leq \left\|\left[\|A_{ij}\|_{ber}\right]\right\|$ and $
Kallol Paul, Pintu Bhunia, Anirban Sen
exaly   +4 more sources

Inequalities Involving Berezin Norm and Berezin Number

Complex Analysis and Operator Theory, 2022
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 $\textbf{ber}(A)$
Kallol Paul, Pintu Bhunia, Anirban Sen
exaly   +3 more sources

Development of the Berezin Number Inequalities

Acta Mathematica Sinica, English Series, 2023
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
Kallol Paul, Pintu Bhunia, Anirban Sen
exaly   +3 more sources

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On Berezin Number Inequalities for Operator Matrices

Acta Mathematica Sinica, English Series, 2021
For a bounded linear operator, acting in the reproducing kernel Hilbert space \(\mathcal{H}=\mathcal{H}(\Omega)\) over some set \(\Omega\), its Berezin symbol \(\tilde{A}\) is defined by \(\tilde{A}(\lambda)=\langle A\tilde{k}_\lambda, \tilde{k}_\lambda \rangle\), where \(\tilde{k}_\lambda\) the normalized reproducing kernel of \(\mathcal{H}\).
Satyajit Sahoo, Nirmal Chandra Rout, Namita Das   +2 more
exaly   +2 more sources

Refinements of some inequalities involving Berezin norms and Berezin number and related questions

Annali Dell'Universita Di Ferrara, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mubariz Garayev
exaly   +2 more sources

Berezin Number and Numerical Radius Inequalities

Vietnam Journal of Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anirban Sen, Kallol Paul
openaire   +1 more source

Berezin number and Berezin norm inequalities via Moore-Penrose inverse

Journal of Pseudo-Differential Operators and Applications
In this article, we establish the Berezin number and Berezin norm inequalities for bounded linear operators on a reproducing kernel Hilbert space using the Moore-Penrose inverse. The inequalities obtained here refine and generalize the earlier inequalities.
Kallol Paul, Anirban Sen
exaly   +3 more sources

Inequalities related to Berezin norm and Berezin number of operators

2022
Summary: The Berezin symbol \(\widetilde{A}\) of an operator \(A\) on the reproducing kernel Hilbert space \(\mathcal{H}(\Omega)\) over some set \(\Omega\) with the reproducing kernel \(k_\lambda\) is defined by \[ \widetilde{A}(\lambda) = \left\langle A \widehat{k}_\lambda,\widehat{k}_\lambda \right\rangle,\; \lambda \in \Omega.
Basaran, Hamdullah, Huban, Mualla Birgul, GÜRDAL, Mehmet   +2 more
openaire   +3 more sources

The weighted and the Davis-Wielandt Berezin number

Operators and Matrices, 2023
Summary: A functional Hilbert space is the Hilbert space of complex-valued functions on some set \(\Theta \subseteq \mathbb{C}\) that the evaluation functionals \(\varphi_\lambda (f) = f\ (\lambda)\), \(\lambda \in \Theta\) are continuous on \(\mathcal{H}\). The Berezin number of an operator \(T\) is defined by \(\mathbf{ber} (T) =\sup\limits_{\lambda \
Garayev, Mubariz T., Bakherad, Mojtaba, Tapdigoglu, Ramiz   +2 more
openaire   +1 more source

Further Berezin Number and Berezin Norm Inequalities for Sums and Products of Operators

Complex Analysis and Operator Theory
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guesba, Messaoud, Barik, Somdatta, Paul, Kallol   +2 more
openaire   +2 more sources