运算符手段、原点和定点方程

Dániel Virosztek
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引用次数: 0

摘要

久保和安藤在 1980 年的开创性工作为我们提供了正算子手段的公理方法。由于他们的公理大多是代数性质的,因此这种方法具有明显的代数色彩。另一方面,从几何的角度出发,考虑正算子锥体上的距离(广义理解),并通过适当的质心概念定义正算子的主题an,也是非常自然的。这种策略通常会导致一个定点方程,从而描述均值的特征。本研究旨在强调代数方法与几何方法相遇的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Operator means, barycenters, and fixed point equations
The seminal work of Kubo and Ando from 1980 provided us with an axiomatic approach to means of positive operators. As most of their axioms are algebraic in nature, this approach has a clear algebraic flavor. On the other hand, it is highly natural to take the geometric viewpoint and consider a distance (understood in a broad sense) on the cone of positive operators, and define the mean of positive operators by an appropriate notion of the center of mass. This strategy often leads to a fixed point equation that characterizes the mean. The aim of this survey is to highlight those cases where the algebraic and the geometric approaches meet each other.
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