$A$-numerical radius : New inequalities and characterization of equalities

Year 2023, Volume: 52 Issue: 5, 1254 - 1262, 31.10.2023

Pintu Bhunia Kallol Paul

https://doi.org/10.15672/hujms.1126384

Abstract

We develop new lower bounds for the $A$-numerical radius of semi-Hilbertian space operators, and applying these bounds we obtain upper bounds for the $A$-numerical radius of the commutators of operators. The bounds obtained here improve on the existing ones. Further, we provide characterizations for the equality of the existing $A$-numerical radius inequalities of semi-Hilbertian space operators.

Keywords

A-numerical radius, A-operator seminorm, semi-Hilbertian space, inequality

Thanks

The first author would like to thank UGC, Govt. of India for the financial support in the form of senior research fellowship under the mentorship of Prof Kallol Paul

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