Rotfel'd type inequalities for norms

Abstract

In this note, we consider some norm inequalities related to the Rotfel'd Trace InequalityTr f (| A + B |) ≤ Tr f (| A |) + f (| B |)for concave functions f : [0, ∞) → [0, ∞) and arbitrary n-by-n matrices. For instance we show that for a large class of non-negative concave functions f (t) and for all symmetric norms we have{norm of matrix} f (| A + B |) {norm of matrix} ≤ sqrt(2) {norm of matrix} f (| A |) + f (| B |) {norm of matrix}and we conjecture that this holds for all non-negative concave functions. © 2010 Elsevier Inc. All rights reserved.