A matrix subadditivity inequality for f(A + B) and f(A) + f(B) Original Research Article

In 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We extend it to all concave functions: Given positive semidefinite matrices A, B and a non-negative concave function f on [0,∞),double vertical barf(A+B)double vertical barless-than-or-equals, slantdouble vertical barf(A)+f(B)double vertical barfor all symmetric norms (in particular for all Schatten p-norms). The case image is connected to some block-matrix inequalities, for instance the operator norm inequalityimagefor any partitioned Hermitian matrix.