论文标题
对操作员系统预测的抽象表征
An abstract characterization for projections in operator systems
论文作者
论文摘要
我们表明，只能使用操作员系统的抽象数据检测到操作员系统中的一组投影。具体来说，我们表明，如果$ p $是运算符系统$ v $的积极收缩，满足某些订单理论条件，那么就存在将$ v $的完整订单嵌入到$ b（h）$映射$ p $中，向投影运营商。此外，运算符系统中的每个抽象预测$ v $都是$ v $的C*-envelope中的诚实投影。使用这种表征，我们为操作员系统提供了一个抽象的表征，这些操作员系统由两个通勤的投影评估措施的家族跨越，并讨论了量子信息理论中的应用。
We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if $p$ is a positive contraction in an operator system $V$ which satisfies certain order-theoretic conditions, then there exists a complete order embedding of $V$ into $B(H)$ mapping $p$ to a projection operator. Moreover, every abstract projection in an operator system $V$ is an honest projection in the C*-envelope of $V$. Using this characterization, we provide an abstract characterization for operator systems spanned by two commuting families of projection-valued measures and discuss applications in quantum information theory.
