In-betweenness: a geometric monotonicity property for operator means

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Abstract

We introduce the notions of in-betweenness and monotonicity with respect to a metric, for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity. We exhibit two classes of non-trivial means that are monotonic with respect to the Euclidean metric. We also show that all Kubo-Ando means are monotonic with respect to the trace metric, which is the natural metric for the geometric mean.

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Publication date Created: 2010-11-29

Article

DOI: 10.1016/j.laa.2011.02.051

ArXiV ID: 1011.6313

SO-VID: d3e20a74-1949-4fd5-80c2-9e0c19ea0c3f

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

History

Custom metadata

ACM classes 15A60

Report No Mittag-Leffler-2010fall

Journal reference Linear Algebra Appl. 438(4), 1769-1778 (2013)

Comments 15 pages; a preliminary version has been presented at the June 2010 ILAS Conference in Pisa, Italy

Categories math.FA math-ph math.MP

ScienceOpen disciplines: Mathematical physics,Mathematical & Computational physics,Functional analysis

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ScienceOpen disciplines: Mathematical physics, Mathematical & Computational physics, Functional analysis

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