Results 11 to 20 of about 10,663,991 (195)
New Inequalities and an Integral Expression for the 𝒜-Berezin Number
Journal of MathematicsThis 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 +3 more
doaj +2 more sources
Berezin number inequalities via convex functions
Filomat, 2022 The Berezin symbol ?A of an operator A on the reproducing kernel Hilbert space H (?) over some set ? with the reproducing kernel k? is defined by ? (?) = ?A k?/||k?||, k?/||k?||?, ? ? ?. The Berezin number of an operator A is defined by ber(A) := sup ?
M. Huban, Hamdullah Başaran, M. Gürdal
semanticscholar +4 more sources
Numerical radius and Berezin number inequality [PDF]
Journal of Mathematical Analysis and Applications, 2022 . We study various inequalities for numerical radius and Berezin number of a bounded linear operator on a Hilbert space. It is proved that the numerical radius of a pure two-isometry is 1 and the Crawford number of a pure two-isometry is 0. In particular,
Satyabrata Majee, Amit Maji, A. Manna
semanticscholar +4 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 +3 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 ...
N. Altwaijry, Kais Feki, N. Minculete
semanticscholar +2 more sources
Advanced refinements of Berezin number inequalities
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2023 For a bounded linear operator $A$ on a functional Hilbert space $\mathcal{H}\left( \Omega\right) $, with normalized reproducing kernel $\widehat {k}_{\eta}:=\frac{k_{\eta}}{\left\Vert k_{\eta}\right\Vert _{\mathcal{H}}},$ the Berezin symbol and Berezin ...
M. Gürdal, Hamdullah Başaran
semanticscholar +3 more sources
Improved inequalities for the Berezin number
Journal of Mathematical Inequalities. A functional Hilbert space is the Hilbert space of complex-valued functions on some set Θ ⊆ C that the evaluation functionals ϕ τ ( f ) = f ( τ ) , τ ∈ Θ are continuous on H . The Berezin number(radius) of an operator T is de fi ned by ber ( T ) = sup τ
Davood Afraz +2 more
semanticscholar +2 more sources
Some extensions of Berezin number inequalities on operators [PDF]
Rocky Mountain Journal of Mathematics, 2021 . In this paper, we establish some upper bounds for Berezin number inequalities including of 2 × 2 operator matrices and their off-diagonal parts.
M. Bakherad +3 more
semanticscholar +4 more sources
Inequalities of generalized Euclidean Berezin number
Filomat, 2022 In this paper, we present several Berezin number inequalities involving extensions of Euclidean Berezin number for n operators. Among other inequalities for (T1,..., Tn) ? B(H) we show that berp p(T1,..., Tn) ?
Fengsheng Chien +3 more
semanticscholar +2 more sources
The weighted and the Davis-Wielandt Berezin number
Operators and Matrices, 2023 . A functional Hilbert space is the Hilbert space of complex-valued functions on some set ⊆ C that the evaluation functionals ( f ) = f ( ) , ∈ are continuous on H .
M. Garayev +2 more
semanticscholar +2 more sources