Results 1 to 10 of about 14,266 (165)

Berezin number inequalities for operators [PDF]

Concrete Operators, 2019
Abstract 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 ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over k} _\lambda } = {{{k_\lambda }} \over {\left\| {{k_\lambda }} \right\|}}$ is the normalized ...
Mojtaba Bakherad, Mubariz Garayev
exaly   +3 more sources

On Berezin norm and Berezin number inequalities for sum of operators

Demonstratio Mathematica
Abstract 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. First, we present some bounds regarding the Berezin number associated with
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

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.
Anirban Sen, Kallol Paul
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 $
Anirban Sen, Kallol Paul
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.
Anirban Sen, Riddhick Birbonshi, Kallol Paul   +2 more
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

Spectral aspects of the Berezin transform [PDF]

, 2020
We discuss the Berezin transform, a Markov operator associated to positive operator valued measures (POVMs), in a number of contexts including the Berezin-Toeplitz quantization, Donaldson's dynamical system on the space of Hermitian products on a complex
Ioos, Louis, Kaminker, Victoria, Polterovich, Leonid, Shmoish, Dor   +3 more
core   +3 more sources

REVERSE INEQUALITIES FOR THE BEREZIN NUMBER OF OPERATORS

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2022
For a bounded linear operator $A$ on a reproducing kernel Hilbert space $\mathcal{H}(Ω)$, with normalized reproducing kernel $\widehat{k}_λ = \frac{k_λ}{\lVert k_λ\lVert}$, the Berezin symbol, Berezin number and Berezin norm are defined respectively by $\widetilde{A}(λ) = \langle A\widehat{k}_λ,\widehat{k}_λ\rangle$, $ber(A) = \sup_{λ\inΩ}\left ...
Garayev, Mubariz, Guediri, Hocine, Altwaijry, Najla   +2 more
openaire   +2 more sources

Complete refinements of the Berezin number inequalities [PDF]

Journal of Mathematical Inequalities, 2019
In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space $\mathcal H=\mathcal H(Ω)$ and also improve them.
Hajmohamadi, Monire, YAMANCI, Ulaş, Lashkaripour, Rahmatollah, Bakherad, Mojtaba   +3 more
openaire   +5 more sources