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A New Family of Semi-Norms Between the Berezin Radius and the Berezin Norm

Acta Applicandae Mathematicae
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Fuad Kittaneh, Mojtaba Bakherad, Cristian Conde   +2 more
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Some new relations between the Berezin number and the Berezin norm of operators

Rocky Mountain Journal of Mathematics, 2022
For a bounded linear operator \(A\) on a reproducing kernel Hilbert space with reproducing kernel \(K(z,w)\), the Berezin symbol, Berezin norm and Berezin number of \(A\) are defined, respectively, by \[ \tilde A(w):=\langle Ak_w,k_w\rangle, \quad \|A\|_{Ber} := \sup_w \|Ak_w\|, \quad \operatorname{ber}(A) :=\sup_w |\tilde A(w)|, \] where \(k_w(z):=K(z,
Çalisir, Irem, SALTAN, Suna, Tapdigoglu, Ramiz   +2 more
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Refinements of some inequalities involving Berezin norms and Berezin number and related questions

Annali Dell'Universita Di Ferrara, 2023
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Mubariz Garayev
exaly   +2 more sources

On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities

Numerical Functional Analysis and Optimization, 2023
In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain
Kallol Paul, Mehmet Gürdal
exaly   +3 more sources

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

Complex Analysis and Operator Theory
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Kallol Paul
exaly   +3 more sources

Norm of Berezin transformon L p space

Journal D'Analyse Mathematique, 2008
Let \(D\) be the unit disc in \(\mathbb C\) equipped with the standard Lebesgue measure \(\mu\). For \(K_\alpha(z, \xi)= (\alpha +1)\frac{(1-| \xi| ^2)^\alpha}{^(1-z\overline{\xi})^{\alpha + 2}}\), the operator \(G_\alpha: L^p(D) \to L^p(D)\), \((G_\alpha f)(z):= \frac1\pi \int_D| K_\alpha(z, \xi)| f(\xi)\,d\mu(\xi)\) is introduced.
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Berezin Number and Norm Inequalities for Operators in Hilbert and Semi-Hilbert Spaces

Mathematics Online First Collections, 2023
Kais Feki, Fuad Kittaneh, Cristian Conde
exaly   +2 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

Schatten-Herz Operators, Berezin Transform and Mixed Norm Spaces

Integral Equations and Operator Theory, 2011
Let ...
Blasco, Oscar, Pérez-Esteva, Salvador
openaire   +1 more source