Some upper bounds for the Berezin number of Hilbert space operators

Abstract

In this paper, we obtain some Berezin number inequalities based on the definition of Berezin symbol. Among other inequalities, we show that if A, B be positive definite operators in B(H), and A B is the geometric mean of them, then ber 2 (A B) ≤ ber A 2 + B 2 2 − 1 2 inf λ∈Ω ζ(k λ), where ζ(k λ) = (A − B)k λ ,k λ 2 , andk λ is the normalized reproducing kernel of the space H for λ belong to some set Ω. A(λ) = Ak λ (z),k λ (z) ,

Inequalities involving Berezin number and $ \alpha $-Berezin norm

“…which was given in [6]. This shows that Theorem 4.1 is an extension of the existing inequality (14).…”

“…For the basic properties and more facts about the Berezin norm and Berezin number, we refer the reader to [4,9,12,14] and the references therein.…”

Davis–Wielandt–Berezin radius inequalities of reproducing kernel Hilbert space operators

“…It is clear from the definition that Ber(A) ⊆ W (A) and so ber(A) ≤ w(A). The Berezin symbols and Berezin number inequalities have been studied by many mathematicians over the years, for the latest and recent results we refer the readers to see [2,8,16,18,20,21,28,30] and the references therein.…”

Davis-Wielandt-Berezin radius inequalities of Reproducing kernel Hilbert space operators

“…It is clear from the definition that Ber(A) ⊆ W (A) and so ber(A) ≤ w(A). The Berezin number inequalities have been studied by many mathematicians over the years, for the latest and recent results we refer the readers to see [1,14,21,23] and the references therein.…”