论文标题
$ c^*$ - 代数上的dixmier类型平均属性的属性
A Dixmier type averaging property of automorphisms on a $C^*$-algebra
论文作者
论文摘要
在他研究von Neumann代数和$ C^*$ - 代数的相对Dixmier属性中，Popa考虑了对$ C^*$ - 代数的某种自动形态性属性，我们在这里称之为强大的平均属性。在本说明中，我们表征了$ C^*$ - 代数具有强大的平均属性时的自动形态。特别是，在自由的情况下，对交换性的$ c^*$ - 代数完全具有该属性的自动形态。具有至少一个奇特状态的Unital可分开的简单$ C^*$ - 代数的自动形态具有强大的平均属性，而当它扩展到$ C^*$的Bi-Dual的有限部分时，代数是外部的，而在简单的，非传统的情况下，强大的平均属性等于外部。 为了说明强大的平均属性的有用性，我们提供了三个示例，在其中我们可以更简单地证明交叉产品$ c^*$ - 代数的现有结果，我们还能够以不同的方向扩展这些结果。
In his study of the relative Dixmier property for inclusions of von Neumann algebras and of $C^*$-algebras, Popa considered a certain property of automorphisms on $C^*$-algebras, that we here call the strong averaging property. In this note we characterize when an automorphism on a $C^*$-algebra has the strong averaging property. In particular, automorphisms on commutative $C^*$-algebras possess this property precisely when they are free. An automorphism on a unital separable simple $C^*$-algebra with at least one tracial state has the strong averaging property precisely when its extension to the finite part of the bi-dual of the $C^*$-algebra is properly outer, and in the simple, non-tracial case the strong averaging property is equivalent to being outer. To illustrate the usefulness of the strong averaging property we give three examples where we can provide simpler proofs of existing results on crossed product $C^*$-algebras, and we are also able to extend these results in different directions.
