欧几里得 Jordan 代数中弱谱集的几何交换原理
Geometric commutation principle for weakly spectral sets in Euclidean Jordan algebras
AI总结：
针对欧几里得 Jordan 代数中谱集几何交换原理仅适用于谱集的局限，本文将其推广至更广泛的弱谱集，证明类似原理并探讨其推论及在优化问题中的应用。
摘要：
Gowda 最近证明的欧几里得 Jordan 代数中的几何交换原理指出，对于欧几里得 Jordan 代数 V 中的任意谱集 E 以及 a∈E，a 与法锥 N_E(a) 中的每个元素强算子交换。此外，该原理可用于在某些优化问题中建立强算子交换关系。鉴于每个谱集都是更广泛的弱谱集类的特例，我们证明了弱谱集的几何交换原理的类似结论，并研究了其推论与应用。
英文摘要：
A geometric commutation principle in Euclidean Jordan algebra, recently proved by Gowda, says that, for any spectral set $E$ in a Euclidean Jordan algebra $V$ and $a \in E$, $a$ strongly operator commutes with every element in the normal cone $N_E(a)$. Further, it can be used to establish strong operator commutativity relations in certain optimization problems. Knowing that every spectral sets are special cases of broader class of weakly spectral sets, we prove an analog of a geometric commutation principle for weakly spectral sets and study its consequences and applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
