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Journal Article
Geometric convexity of an operator mean
2020
Overview
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(tp)for allp>1,then σ is called a pmi mean. Our main interest is the class of pmi means (denoted by PMI). To study PMI, the operator means σ satisfying fσ(xy)≤fσ(x)fσ(y)(x,y>0)are considered in this paper. The set of such means (denoted by GCV) includes certain significant examples and is included in PMI. The main result presented in this paper is that GCV is a proper subset of PMI. In addition, we investigate certain operator-mean classes including PMI.
Publisher
Springer Nature B.V
Subject
