Convex multivariate operator means
Convex multivariate operator means
复制标题
凸多元算子均值
DOI：
10.1016/j.laa.2018.11.032
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发表时间：
2019
影响因子：
1.1
通讯作者：
Hansen Frank
中科院分区：
文献类型：
--
作者：
Hansen Frank
证明了一个由泛函微积分生成的迹函数在正定矩阵的黎曼流形上是测地线凸的，当且仅当它在正数上是测地线凸的。通过研究相对于汤普森度规的收缩下不动点的均值类，有助于多元算子均值的分析。尽管这些方法很强大，但它们主要依赖于单调性。我们发展了证明不一定单调的多元算子的存在性的新方法。
We prove that a trace function, generated by the functional calculus, is geodesically convex in the Riemannian manifold of positive definite matrices, if and only if it is geodesically convex in positive numbers. The analysis of multivariate operator means is facilitated by the study of classes of means that are fix-points under a contraction with respect to the Thompson metric. Although such methods are powerful, they crucially depend on monotonicity. We develop new techniques to prove existence of multivariate operator means that are not necessarily monotone.