A General Framework for Extending Means to Higher Orders

Details A General Framework for Extending Means to Higher Orders A General Framework for Extending Means to Higher Orders

2006-12-11

arxiv.org/abs/math/0612293v1

Mathematics

Functional Analysis

35 pages

Scientific paper

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.

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