JOINTLY SUBADDITIVE MAPPINGS INDUCED BY OPERATOR CONVEX FUNCTIONS

In this paper, we study jointly subadditive mappings induced by operator convex functions and generalized inverses of positive linear maps. We formulate conditions under which the inequalities T fT(-)(Sigma(n)(k=1) T(k)A(k)) <= Sigma(n)(k=1) T(k)f(A(k)) and T fT(-)Phi(A) <= Phi(f (A)) hold, where f is an operator convex function, A,A(k) is an element of B(H) with Hilbert space H, and T, T-k and Phi are positive linear maps (not necessarily unital) on B(H), with a (reflexive) generalized inverse T- of T. We also show that the transformation T fT(-) (B) is jointly subadditive in (T, B) and antimonotone in T(I).