论文标题
紧凑型操作员和多数化代数上的非线性迹线
Non-linear traces on the algebra of compact operators and majorization
论文作者
论文摘要
我们在紧凑型操作员的代数上研究Choquet类型和Sugeno类型的非线性痕迹。他们具有某些部分添加性。我们表明，这些部分添加性分别表征了Choquet类型和Sugeno类型的非线性痕迹。 Choquet类型的非线性痕迹与多数化理论之间存在密切的关系。我们研究Choquet类型的非线性痕迹的跟踪类操作员。更普遍地，我们讨论Schatten-Von Neumann $ P $ -Class Operators for Choquet类型的非线性痕迹。我们确定它们何时形成Banach空间。这是针对紧凑型操作员代数上的非线性痕迹的非交通整合理论的尝试。我们还考虑了Sugeno类型的非线性痕迹的三角形不等式。
We study non-linear traces of Choquet type and Sugeno type on the algebra of compact operators. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively. There exists a close relation between non-linear traces of Choquet type and majorization theory. We study trace class operators for non-linear traces of Choquet type. More generally we discuss Schatten-von Neumann $p$-class operators for non-linear traces of Choquet type. We determine when they form Banach spaces. This is an attempt of non-commutative integration theory for non-linear traces of Choquet type on the algebra of compact operators. We also consider the triangle inequality for non-linear traces of Sugeno type.
