J-厄米特矩阵锥上的Kubo Ando均值
Kubo Ando Means on the Cone of J Hermitian Matrices
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中文总结 AI 辅助
本文将Kubo-Ando均值理论扩展到正四元数厄米特矩阵锥，并针对J-厄米特正矩阵锥建立类似框架，证明其均值与算子单调函数一一对应，扩展了经典特征到不定情形。
中文摘要 AI 辅助
Kubo-Ando均值理论建立了正半轴上算子均值与算子单调函数之间的基本对应关系。本文首先将该理论扩展到正四元数厄米特矩阵锥，建立Kubo和Ando主要结果的四元数类比。随后，针对与不定内积相关的J-厄米特正矩阵锥，开发了类似框架，特别证明该锥上的Kubo-Ando均值仍与算子单调函数一一对应，从而将经典特征刻画扩展到不定情形。
英文摘要
The theory of Kubo-Ando means provides a fundamental correspondence between operator means and operator monotone functions on the positive half-line. In this paper, we first extend this theory to the cone of positive quaternionic Hermitian matrices, establishing quaternionic analogues of the main results of Kubo and Ando. We then develop an analogous framework for the cone of J-Hermitian positive matrices associated with an indefinite inner product. In particular, we prove that Kubo-Ando means on this cone are again in one-to-one correspondence with operator monotone functions, thereby extending the classical characterization to this indefinite setting.
