Relative operator entropy properties related to some weighted metrics

Abstract

In recent decades, intensive research has been devoted to the study of various operator entropies.  In this work, we investigate the properties of the parameterized relative operator entropy Sp(A | B) acting on positive definite matrices with respect to weighted Hellinger and Alpha Procrustes distances. In particular, we investigate  estimation of the distance between the entropy Sp(A | B) and certain standard means.