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

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,

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