Extension of Rotfel'd Theorem

Let f (t) be a non-negative concave function on the positive half-line. Given an arbitrary partitioned positive semi-definite matrix, we show that parallel to f([A X X* B])parallel to <= parallel to f(A)parallel to + parallel to f(B)parallel to for all symmetric (i.e. unitarily invariant) norms. This characterization of concave functions extends a famous trace inequality of Rotfel'd, Trf(A+B) <= Tr f(A) _ Tr f(B) and contains several classical matrix inequalities. (C) 2011 Elsevier Inc. All rights reserved.