Results 1 to 10 of about 83 (64)

On Berezin norm and Berezin number inequalities for sum of operators

Demonstratio Mathematica
The aim of this study is to obtain several inequalities involving the Berezin number and the Berezin norm for various combinations of operators acting on a reproducing kernel Hilbert space.
Najla Altwaijry, Kais Feki
exaly   +4 more sources

A new mean-Berezin norm for operators in reproducing kernel Hilbert spaces

Journal of Inequalities and Applications
A functional Hilbert space is defined as the Hilbert space K $\mathcal{K}$ of complex-valued functions defined on a set Θ. In this space, the evaluation functionals ψ ε ( h ) = h ( ε ) $\psi _{\varepsilon}(h) = h(\varepsilon )$ , for ε ∈ Θ $\varepsilon ...
Mojtaba Bakherad, Bakherad Mojtaba
exaly   +3 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   +2 more
exaly   +3 more sources

Some New Estimates for the Berezin Number of Hilbert Space Operators

Axioms, 2022
In this paper, we have developed new estimates of some estimates involving the Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space HΩ.
Najla Altwaijry, Nicusor Minculete, Kais Feki   +2 more
exaly   +3 more sources

New Inequalities and an Integral Expression for the 𝒜-Berezin Number

Journal of Mathematics
This work examines a reproducing kernel Hilbert space XF,·,· constructed on a nonempty set F. Our investigation focuses on the A-Berezin number and the A-Berezin norm, where A denotes a positive bounded linear operator acting on XF.
Salma Aljawi, Ahad Alotaibi, Cristian Conde, Kais Feki   +3 more
doaj   +2 more sources

Numerical radius, Berezin number, and Berezin norm inequalities for sums of operators

Turkish Journal of Mathematics, 2023
The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space.
Najla Altwaijry, Nicusor Minculete, Kais Feki   +2 more
exaly   +2 more sources

Inequalities involving Berezin number and $ \alpha $-Berezin norm

Discrete and Continuous Dynamical Systems - Series S
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fugen Gao
exaly   +2 more sources

Berezin number and Berezin norm inequalities for operator matrices

Linear and Multilinear Algebra
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   +2 more
exaly   +3 more sources

New Approach to Generalized Berezin Norms and Rigorous Operator Bounds

Mathematics
Let HΘ,⟨·,·⟩ be a reproducing kernel Hilbert space over a non-empty set Θ, and let A be a non-zero positive operator on HΘ. This operator induces a semi-inner product given by ⟨ξ,η⟩A=⟨Aξ,η⟩ for all ξ,η∈HΘ, with the associated seminorm ∥ξ∥A=⟨ξ,ξ⟩A.
Ghadah Albeladi, Kais Feki, Hala H. Taha
doaj   +2 more sources

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, Paul Kallol
exaly   +3 more sources