论文标题
操作员代数的最小界限
Minimal boundaries for operator algebras
论文作者
论文摘要
我们研究Unital Operator代数的边界。这些是一组不可约的$*$ - 完全捕获给定子代数的空间标准达到的表示。从经典上讲，Choquet边界是函数代数的最小边界，它与峰值点的集合相吻合。我们研究了Choquet边界的非交通性对应物的最小化问题，并表明最小性等于我们所谓的Bishop属性。并非每个操作员代数都有主教财产，但是我们展示了这样做的类型。在我们的整个分析中，我们为操作员代数利用了峰值点的各种非交通概念。当专门针对$ c^*$ - 代数的设置时，我们的技术使我们能够提供新的证据，证明最近对这些$ c^*$ - 代数仅承认只有有限维度的不可减至的表示形式。
We study boundaries for unital operator algebras. These are sets of irreducible $*$-representations that completely capture the spatial norm attainment for a given subalgebra. Classically, the Choquet boundary is the minimal boundary of a function algebra and it coincides with the collection of peak points. We investigate the question of minimality for the non-commutative counterpart of the Choquet boundary and show that minimality is equivalent to what we call the Bishop property. Not every operator algebra has the Bishop property, but we exhibit classes of examples that do. Throughout our analysis, we exploit various non-commutative notions of peak points for an operator algebra. When specialized to the setting of $C^*$-algebras, our techniques allow us to provide a new proof of a recent characterization of those $C^*$-algebras admitting only finite-dimensional irreducible representations.
