论文标题
有限集的耐受性关系的操作员系统
Operator systems for tolerance relations on finite sets
论文作者
论文摘要
我们研究了一类有限维操作员系统的双重双重，即与有限集或与图形相关的操作员系统相关的耐受性关系相关的运算符系统。如果与这些操作员系统相关的图形是和弦，我们可以找到坐在有限维$ C^*$ - 代数的内部的混凝土实现。然后，我们使用这些具体实现来计算串联案例中这些双重的$ c^*$ - 信封，传播数字和极端射线。最后，我们通过将结果应用于频带矩阵的操作员系统来体现我们的结果。
We study the duals of a certain class of finite-dimensional operator systems, namely the class of operator systems associated to tolerance relations on finite sets or equivalently the class of operator systems that are associated with graphs. In the case where the graphs associated with these operator systems are chordal we are able to find concrete realizations of their duals as sitting inside of finite-dimensional $C^*$-algebras. We then use these concrete realizations to compute the $C^*$-envelopes, propagation numbers and extremal rays of these duals in the chordal case. Finally, we exemplify our results by applying them to operator systems of band matrices.
