Results 1 to 10 of about 3,734 (119)

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

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, Anirban Sen
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, Kais Feki, Nicusor Minculete   +2 more
exaly   +3 more sources

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

Turkish Journal of Mathematics, 2023
Summary: 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, Kais Feki
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 $
Anirban Sen, Kallol Paul
exaly   +3 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
doaj   +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 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.
Anirban Sen, Riddhick Birbonshi, Kallol Paul   +2 more
exaly   +3 more sources

A New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Number Inequalities

Complex Analysis and Operator Theory
11 ...
Pintu Bhunia, Raj Kumar Nayak
exaly   +3 more sources

A Generalized Norm on Reproducing Kernel Hilbert Spaces and Its Applications

Axioms, 2023
The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm of bounded linear ...
Najla Altwaijry, Kais Feki, Nicuşor Minculete   +2 more
doaj   +1 more source