Abstract
It is known that for every and every k-tuple of positive invertible operators , the Ando–Hiai type inequality for operator power means holds, where is the operator norm and is the operator power mean. However it is not known any relation between and under the Löwner partial order. In this paper, we present some Ando–Hiai type inequalities for operator power means, which give a relation between and for every unital positive linear map Φ. In addition, we obtain a difference counterpart to the information monotonicity.
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