Title

On the monotonicity of weighted power means for matrices

Document Type

Article

Publication Date

8-15-2017

Subject Area

ARRAY(0x5575af9b49a8)

Abstract

In this article, we provide an alternate proof of the fact that the weighted power means μp(A,B,t)=(tAp+(1−t)Bp)1/p, 1≤p≤2 satisfy Audenaert's “in-betweenness” property for positive semidefinite matrices. We show that the “in-betweenness” property holds with respect to any unitarily invariant norm for p=1/2 and with respect to the Euclidean metric for p=1/4. We also show that the only Kubo–Ando symmetric mean that satisfies the “in-betweenness” property with respect to any metric induced by a unitarily invariant norm is the arithmetic mean. Finally, for p=6 we give a counterexample to a conjecture by Audenaert regarding the “in-betweenness” property.

Publication Title

Linear Algebra and Its Applications

Volume

527

First Page

128

Last Page

140

Digital Object Identifier (DOI)

10.1016/j.laa.2017.04.003

ISSN

00243795

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