On the Ando-Hiai property for spectral geometric means

Abstract

In this paper, we consider a two-variable operator function that includes two weighted spectral geometric means, and show fundamental properties of the operator function. Moreover, it satisfies the Ando-Hiai type inequality under some restricted conditions. As an application, we show the log-majorization relations and norm inequalities for the spectral geometric means of positive definite matrices.

Submitted to Linear Algebra and its Applications