论文标题
Schatten的Hilbert Modules commutative c* - 代数
Schatten classes for Hilbert modules over commutative C*-algebras
论文作者
论文摘要
我们通过Abelian $ C^*$ - 代数定义了Hilbert模块上可相邻运营商的Schatten类。 Hilbert Space Case的许多关键功能都延续了出来。特别是，Schatten类构成了紧凑型操作员的双面理想，并配备了Banach Norm和$ c^*$ - 具有预期属性的价值痕迹。对于琐碎的希尔伯特捆绑包，我们表明我们的沙滕级操作员可以用Schatten-norm连续图从基本空间从基本空间识别到Hilbert Space纤维上的Schatten类，并带有光纤迹线。作为应用程序，我们介绍了$ C^*$ - 有价值的Fredholm决定因素和操作员Zeta功能，并在交换设置中提出了$ p $ -p $的概念。
We define Schatten classes of adjointable operators on Hilbert modules over abelian $C^*$-algebras. Many key features carry over from the Hilbert space case. In particular, the Schatten classes form two-sided ideals of compact operators and are equipped with a Banach norm and a $C^*$-valued trace with the expected properties. For trivial Hilbert bundles, we show that our Schatten-class operators can be identified bijectively with Schatten-norm-continuous maps from the base space into the Schatten classes on the Hilbert space fiber, with the fiberwise trace. As applications, we introduce the $C^*$-valued Fredholm determinant and operator zeta functions, and propose a notion of $p$-summable unbounded Kasparov cycles in the commutative setting.
