A converse inequality of higher order weighted arithmetic and geometric means of positive definite operators

摘要

In this paper we consider weighted arithmetic and geometric means of higher orders constructed by the symmetrization method appeared in Ando-Li-Mathias's definition of multi-variable geometric means and the arithmetic-geometric mean inequality of higher order weighted version. We establish a converse inequality of higher order weighed arithmetic and geometric means via Specht ratio. (c) 2007 Elsevier Inc. All rights reserved.