Year: 2006
Type: preprint
Abstract: In this paper we study the problem of extending means to means of higher order. We show how higher order means can be inductively defined and established in general metric spaces, in particular, in convex metric spaces. As a particular application, we consider the positive operators on a Hilbert space under the Thompson metric and show that the operator logarithmic mean admits extensions of all higher orders, thus providing a positive solution to a problem of Petz and Temesi.
Source: arXiv (Cornell University)
Authors: Lawson, Jimmie, Lim, Yongdo
Institutions: Louisiana State University, Kyungpook National University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950029692