Complete refinements of the Berezin number inequalities

2020/03/22 by Bakherad, M., Lashkaripour, R., Hajmohamadi, M. +1
#30E20 #47A12 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A30 #Secondary 15A60

paper · doi:10.48550/arxiv.2003.09826

Abstract

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 acting on a reproducing kernel Hilbert space \mathcal H=\mathcal H(Ω) and also improve them. Among other inequalities, it is shown that if A,B∈ \mathcal B(\mathcal H) such that |A|B=B^*|A|, f and g are nonnegative continuous functions on [0,∞) satisfying f(t)g(t)=t (t≥ 0), then amp;ber^p(AB)≤ r^p(B)×
amp;(ber (\frac1αf^αp(|A|)+\frac1βg^βp(|A^*|))-r₀(⟨ f²(|A|)k_λ,k_λ⟩^αp/4 -⟨ g²(|A^*|)k_λ,k_λ⟩^βp/4)²) for every p≥ 1, α≥β>1 with \frac1α+\frac1β=1, βp≥2 and r₀=min\\frac1α,\frac1β\.

Related

• Some Berezin number inequalities for operator matrices
• Berezin number inequalities for Hilbert space operators
• Inequalities involving Berezin norm and Berezin number
• Reverse inequalities for the Berezin number of operators
• Improvements of Berezin number inequalities