Accretive operators and Cassels inequality

Let a,b>0a,b>0 and let Z∈Mn(R)Z∈Mn(R) such that ZZ lies into the operator ball of diameter [aI,bI][aI,bI]. Then for all positive definite A∈Mn(R)A∈Mn(R),Tr|AZ|⩽a+b2abTrAZ.Several related reverse inequalities are considered, extending some known results.