Let A be a positive bounded operator on a Hilbert space (H,<⋅,⋅>). The semi-inner product<
x, y> A:=< A x, y>, x, y∈ H induces a semi-norm‖⋅‖ A on H. Let‖ T‖ A and w A (T) …

The Berezin symbol à of an operator A acting on the reproducing kernel Hilbert space H= H
(Ω) H= H (Ω) over some (nonempty) set is defined by ̃ A (λ)=\left ⟨ A ̂ k_ λ, ̂ k_ λ\right ⟩ …

In this article, we introduce the definition of the weighted numerical radius ω _ ν (T) ω ν (T) of
a Hilbert space operator T, and present. many interesting properties of this newly defined …

In this paper, we generalize several Berezin number inequalities involving product of
operators, which acting on a Hilbert space H (Ω). Among other inequalities, it is shown that if …

In this paper, we prove reverse inequalities for the so-called Berezin number of some
operators. Also, by using the classical Jensen and Young inequalities, we obtain upper …

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 …

The goal of this study is to refine some numerical radius inequalities in a novel way. The
new improvements and refinements purify some famous inequalities pertaining to Hilbert …

In this work, the concept of the Davis-Wielandt Berezin number is introduced. Some upper
and lower bounds for the Davis-Wielandt Berezin number are introduced. A connection …

The weighted and the Davis-Wielandt Berezin number Page 1 Operators and Matrices
Volume 17, Number 2 (2023), 469–484 doi:10.7153/oam-2023-17-31 THE WEIGHTED AND …

This paper proves several new inequalities for the Euclidean operator radius, which refine
some recent results. It is shown that the new results are much more accurate than the …