论文标题
一般对称的kubo-ando手段的分歧中心解释以及相关的加权多元操作员手段
A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means
论文作者
论文摘要
众所周知，特殊的Kubo-Ando操作员意味着接纳分歧中心的解释，此外，它们也是正方形误差估计器的某些指标的均值误差估计器。在本文中，我们为每个对称的kubo-ando提供了分歧中心的解释。对称的这种表征自然会导致大量对称的Kubo-Ando均值的加权和多元版本的定义。我们研究了这些加权多变量手段的基本特性，并特别注意，在几何的特殊情况下，我们恢复了加权$ \ MATHCAL {a} \＃\ MATHCAL {h} $ - 金，Lawson和Lim引入的含义。
It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted $\mathcal{A} \# \mathcal{H}$-mean introduced by Kim, Lawson, and Lim.
