论文标题
混合和插值的参数序列平均值
Mixture and interpolation of the parameterized ordered means
论文作者
论文摘要
Loewner局部顺序在公开式可逆操作员的开放凸锥中在度量拓扑和操作员不平等中起着非常重要的作用。在本文中，我们考虑了具有均匀性和属性的积极可逆运算符的有序手段的家族g，例如单调性，关节凹性和算术 - 谐波 - 谐波加权的平均不等式。与分解平均值相似，我们构建了一个参数化有序的平均值，并根据Loewner顺序比较了两种类型的参数化有序均值混合物。我们还显示了两个与功率平均值相关的参数级别均值均值，单调插值给定两个参数化有序均值的关系。
Loewner partial order plays a very important role in metric topology and operator inequality on the open convex cone of positive invertible operators. In this paper we consider a family G of the ordered means for positive invertible operators equipped with homogeneity and properties related to the Loewner partial order such as the monotonicity, joint concavity, and arithmetic-G-harmonic weighted mean inequalities. Similar to the resolvent average, we construct a parameterized ordered mean and compare two types of the mixture of parameterized ordered means in terms of the Loewner order. We also show the relation between two families of parameterized ordered means associated with the power mean, monotonically interpolating given two parameterized ordered means.
