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December 2021 Some extensions of Berezin number inequalities on operators
Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour, Satyajit Sahoo
Rocky Mountain J. Math. 51(6): 1941-1951 (December 2021). DOI: 10.1216/rmj.2021.51.1941

Abstract

We establish some upper bounds for Berezin number inequalities including inequalities for 2×2 operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if T=[0XY0], then

berr(T)2r2(ber(f2r(|X|)+g2r(|Y|))+ber(f2r(|Y|)+g2r(|X|)))2r2inf(kλ1,kλ2)=1η(kλ1,kλ2),

where X, Y are bounded linear operators on a Hilbert space =(Ω), r1, f, g are nonnegative continuous functions on [0,) satisfying the relation f(t)g(t)=t (t[0,)) and

η(kλ1,kλ2)=((f2r(|X|)+g2r(|Y|))kλ2,kλ212(f2r(|Y|)+g2r(|X|))kλ1,kλ112)2.

Citation

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Mojtaba Bakherad. Monire Hajmohamadi. Rahmatollah Lashkaripour. Satyajit Sahoo. "Some extensions of Berezin number inequalities on operators." Rocky Mountain J. Math. 51 (6) 1941 - 1951, December 2021. https://doi.org/10.1216/rmj.2021.51.1941

Information

Received: 1 January 2021; Revised: 24 February 2021; Accepted: 2 April 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1941

Subjects:
Primary: 47A30
Secondary: 30E20 , 47A12 , 47A60

Keywords: Berezin number , Berezin symbol , diagonal operator matrices , off-diagonal part

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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