GENERALIZATIONS OF HEINZ MEAN OPERATOR INEQUALITIES INVOLVING POSITIVE LINEAR MAP.

In this paper, we study the Heinz mean inequalities of two positive operators involving positive linear map. We obtain a generalized conclusion based on operator Diaz-Metcalf type inequality. The conclusion is presented as follows: Let Φ be a unital positive linear map, if 0 < m1 2 ≤ A ≤ M1 2 and 0 < m2 2 ≤ B ≤ M22 for some positive real numbers m1 ≤ M1, m2 ≤ M2, then for α ϵ [0; 1] and p ≥ 2, the following inequality holds : ( M2m2/ M1m1 Φ(A) + Φ(B))p ≤2-(p+4) [M2m2(M1 2 + m1 2) +M1m1(M2 2 + m2 2) /min{(M1m1) 3-α/2 (M2m2) 1+α/2, (M1m1) 2+α/2 (M2m2)2-α/2}2p Φp(Hα(A;B)). [ABSTRACT FROM AUTHOR]