Asymmetric Choi–Davis inequalities

Abstract

ABSTRACT Let Φ be a unital positive linear map and let A be a positive invertible operator. We prove that there exist partial isometries U and V such that and hold under some mild operator convex conditions and some positive numbers r. Further, we show that if is operator concave, then In addition, we give some counterparts to the asymmetric Choi–Davis inequality and asymmetric Kadison inequality. Our results extend some inequalities due to Bourin–Ricard and Furuta.