Results 1 to 10 of about 1,385 (141)

Berezin number inequalities for operators [PDF]

Concrete Operators, 2019
The Berezin transform à of an operator A, acting on the reproducing kernel Hilbert space ℋ = ℋ (Ω) over some (non-empty) set Ω, is defined by Ã(λ) = 〉Aǩ λ, ǩ λ〈 (λ ∈ Ω), where k⌢λ=kλ‖kλ‖${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown ...
Mojtaba Bakherad
exaly   +3 more sources

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, Pintu Bhunia, Anirban Sen   +2 more
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   +2 more
exaly   +3 more sources

New estimations for the Berezin number inequality [PDF]

Journal of Inequalities and Applications, 2020
In this paper, by the definition of Berezin number, we present some inequalities involving the operator geometric mean. For instance, it is shown that if X , Y , Z ∈ L ( H ) $X, Y, Z\in {\mathcal{L}}(\mathcal{H})$ such that X and Y are positive operators,
Mojtaba Bakherad, Ulas Yamancı
doaj   +4 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

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

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

A-BEREZIN NUMBER OF OPERATORS

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2022
Summary: We introduce the notions \((A,r)\)-adjoint of operators and \(A\) Berezin number of operators on the reproducing kernel Hilbert space and prove some inequalities for \(A\)-Berezin number of operators. Some other related questions are also discussed.
GÜRDAL, Mehmet, Basaran, Hamdullah
openaire   +4 more sources

Berezin Yarıçapı İçin Diğer Eşitsizlikler

Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2023
İşlevsel Hilbert uzayları, istatistik, yaklaşım teorisi, grup temsili teorisi, vb. dahil olmak üzere birçok alanda ortaya çıkar. İşlevsel Hilbert uzay sayesinde tanımlanan Berezin dönüşümü ise, düzgün fonksiyonları analitik fonksiyonların Hilbert ...
Mehmet Gürdal, Hamdullah Başaran
doaj   +1 more source