Abstract
Let A,B, and X be bounded linear operators on a separable Hilbert space such that A,B are positive, X ? ?I, for some positive real number ?, and ? ? [0,1]. Among other results, it is shown that if f(t) is an increasing function on [0,?) with f(0) = 0 such that f(?t) is convex, then ?|||f(?A + (1-?)B) + f(?|A-B|)|||?|||?f(A)X + (1-?)Xf (B)||| for every unitarily invariant norm, where ? = min (?,1-?). Applications of our results are given.
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