An integral representation of operator means via the power means and an application to the Ando-Hiai inequality

Yamazaki, Takeaki

doi:10.48550/arxiv.1803.04630

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2019

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“…From the above discussion, the problem whether P M I is a proper subset of P M I ∞ arises (cf. [15]). We provide an answer to this problem.…”

Section: Resultsmentioning

confidence: 99%

Geometric convexity of an operator mean

Wada

2019

Positivity

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Let σ be an operator mean in the sense of Kubo and Ando. If the representation function fσ of σ satisfies fσ(t) p ≤ fσ(t p ) for all p > 1, then σ is called a pmi mean. Our main interest is the class of pmi means (denoted by P M I). To study P M I, the operator mean σ, whereinis considered in this paper. The set of such means (denoted by GCV ) includes certain significant examples and is contained in P M I. The main result presented in this paper is that GCV is a proper subset of P M I.In addition, we investigate certain operator-mean classes, which contain

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“…From the above discussion, the problem whether P M I is a proper subset of P M I ∞ arises (cf. [15]). We provide an answer to this problem.…”

Section: Resultsmentioning

confidence: 99%