论文标题
外围泊松边界
Peripheral Poisson Boundary
论文作者
论文摘要
结果表明，von Neumann代数上的Unital完全正面图的外围特征向量产生的操作员空间具有$ C^*$ - 代数结构。这通过包括单位圆中包含的地图的点光谱来扩展非交通泊松边界的概念。主要成分是扩张理论。该理论为新产品提供了一个简单的公式。该概念对我们对量子动态的理解有影响。例如，显示出在离散量子动力学中的外围泊松边界仍然不变。
It is shown that the operator space generated by peripheral eigenvectors of a unital completely positive map on a von Neumann algebra has a $C^*$-algebra structure. This extends the notion of non-commutative Poisson boundary by including the point spectrum of the map contained in the unit circle. The main ingredient is dilation theory. This theory provides a simple formula for the new product. The notion has implications to our understanding of quantum dynamics. For instance, it is shown that the peripheral Poisson boundary remains invariant in discrete quantum dynamics.
