Ando-Hiai and Golden-Thomspon inequalities

Abstract

The original Ando-Hiai and Golden-Thompson inequalities present comparisons for the operator geometric mean ♯ v when 0 ≤ v ≤ 1. Our main target in this article is to study these celebrated inequalities for means other than the geometric mean and for the geometric mean when v ∈ [0, 1].