Hermitian operators and convex functions

  • Jean-Christophe Bourin
  • Published 2005

Abstract

We establish several convexity results for Hermitian matrices. For instance: Let A, B be Hermitian and let f be a convex function. If X and Y stands for f({A+B}/2 and {f(A) + ff(B)}/2 respectively, then there exist unitaries U , V such that X ≤ UY U∗ + V Y V ∗ 2 . This is nothing but the matrix version of the scalar convexity inequality f ( a+ b 2 ) ≤ f(a… (More)

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