论文标题
反述对正态度一度地图的扩展性的反例
Counterexamples to the extendibility of positive unital norm-one maps
论文作者
论文摘要
Arveson的扩展定理可以确保在操作员系统上定义的每个完全正面的映射可以扩展到包含它的整个C*-Algebra上定义的完全正面的映射。一个类似的陈述，其中已知完全阳性被阳性代替是错误的。一个自然的问题是，扩展性是否仍然可以适用于满足更强条件的正图，例如Unital和Nord 1。在这里，我们提供了三个反例，表明在矩阵代数的操作员子系统上定义的正标准一个Unital地图不能扩展到完整Matrix Algebra的正面地图。第一个反示例是具有单位标准的不可扩展的正值映射，第二个反例是在真实操作员空间上的不可扩展的正静电轴测，而第三个反例是复杂操作员空间上不可延迟的正值均值。
Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by positivity is known to be false. A natural question is whether extendibility could still hold for positive maps satisfying stronger conditions, such as being unital and norm 1. Here we provide three counterexamples showing that positive norm-one unital maps defined on an operator subsystem of a matrix algebra cannot be extended to a positive map on the full matrix algebra. The first counterexample is an unextendible positive unital map with unit norm, the second counterexample is an unextendible positive unital isometry on a real operator space, and the third counterexample is an unextendible positive unital isometry on a complex operator space.
