Asymmetric Choi--Davis inequalities

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 thathold under some mild operator convex conditions and some positive numbers r.Further, we show that if f 2 is operator concave, thenIn 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.