Extension of the furuta inequality and Ando-Hiai log-majorization

Abstract

Ando and Hiai have obtained many excellent log majorization results for power means of positive semidefinite matrices. One of these results ensures matrix-norm inequalities for unitarily invariant norms, which are considered as complementary to the Golden-Thompson inequality. Firstly, we show an extension of the Furuta inequality by using itself. Secondary, by using techniques due to Ando and Hiai and also using this extension of the Furuta inequality, we extend some results on log majorization.