Some extensions of Berezin number inequalities on operators

2023/01/16 by Mojtaba Bakherad, Monire Hajmohamadi, Bakherad, Mojtaba +5
Mathematics · Computer Science · #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2301.06603

Abstract

In this paper, we establish some upper bounds for Berezin number inequalities including of 2× 2 operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if T=[0 · amp;X, Y · amp;0], then ber^r(T)≤ 2^r-2(ber(f^2r(|X|)+g^2r(|Y^*|))+ber(f^2r(|Y|)+g^2r(|X^*|)))
-2^r-2 inf_‖(k_λ₁,k_λ₂)‖=1 η(k_λ₁,k_λ₂), where η(k_λ₁, k_λ₂) = (⟨(f^2r(|X|)+g^2r(|Y^*|))k_λ₂,k_λ₂⟩^(1)/(2)-⟨ (f^2r(|Y|)+g^2r(|X^*|))k_λ₁,k_λ₁⟩^(1)/(2))², X, Y are bounded linear operators on a Hilbert space \mathcal H=\mathcal H(Ω), r≥ 1 and f, g are nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t)=t (t∈[0, ∞)).

Related

• Some Berezin number inequalities for operator matrices
• Berezin number inequalities for Hilbert space operators
• Complete refinements of the Berezin number inequalities
• Improvements of Berezin number inequalities
• Development of the Berezin number inequalities