$A$-numerical radius inequalities and $A$-translatable radii of semi-Hilbert space operators

Abstract

We develop $A$-numerical radius inequalities of the product and the
commutator of semi-Hilbert space operators using the notion of $A$-numerical
radius distance and $A$-seminorm distance. Further, we introduce a pair of
translatable radii of semi-Hilbert space operators in the direction of
another operator and obtain related inequalities which generalize the
relevant inequalities studied in the setting of Hilbert space.