ANDO’S THEOREM FOR HADAMARD PRODUCTS AND OPERATOR MEANS

Abstract

First we see that Ando’s inequality A ∗ B ≥ (A#B) ∗ (A#B) gives a characterization of the geometric operator mean #, where ∗ is the Hadamard product. Extending this, we discuss inequalities for operator means and the Hadamard product. Moreover we show monotone convergence theorems including such inequalities.