In this paper, we provide a new norm (α-Berezin norm) on the space of all bounded linear
operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin …

We establish new upper bounds for the Berezin number and Berezin norm of operator
matrices, which are refinements of existing bounds. Among other bounds, we prove that if …

Abstract Let (H Ω,<⋅,⋅>) be the reproducing kernel Hilbert space over some (non-empty) set
Ω. Let k ̂ λ and k ̂ μ denote two normalized reproducing kernels of H Ω. The Berezin …

In this paper, we give several refinements of Berezin norm and Berezin number inequalities
of bounded linear operators defined on a reproducing kernel Hilbert space. In particular, we …

A functional Hilbert space is the Hilbert space ℋ of complex-valued functions on some set
Θ⊆ C such that the evaluation functionals φ τ (f)= f (τ), τ∈ Θ, are continuous on ℋ. The …

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 …

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 …

For a bounded linear operator T on a Hilbert space H, the Berezin symbol (or Berezin
transform) of T is the bounded function T~ on a set Θ defined by T~ τ= T k^ τ z, k^ τ z for all …

In this article, we conduct a comparative study of Crawford numbers and minimum moduli of
bounded linear operators on Hilbert spaces. We provide a simple and distinct proof for the …

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 …