Improvements of Berezin number inequalities

2018/05/08 by Hajmohamadi, Monire, Lashkaripour, Rahmatollah, Bakherad, Mojtaba
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1805.03231

Abstract

In this paper, we generalize several Berezin number inequalities involving product of operators. For instance, we show that if A, B are positive operators and X is any operator, then ber^r(H_α(A,B))amp;≤\frac‖X‖^r2ber(A^r+B^r)amp;≤\frac‖X‖^r2ber(αA^r+(1-α)B^r)+ber((1-α)A^r+αB^r), where H_α(A,B)=\fracA^αXB^1-α+A^1-α XB^α2, 0≤α≤1 and r≥2.

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• Complete refinements of the Berezin number inequalities
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• Inequalities involving Berezin norm and Berezin number