We give an exposition of two fundamental results of the theory of crossed products. One of these states that every regular representation of a reduced crossed product is faithful whenever the underlying Hilbert space representation of the $C^{\ast }$-algebra that together with an automorphism group gives rise to the crossed product is faithful. The other result states that a full and a reduced crossed products coincide whenever their common underlying automorphism group is amenable.

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关于交叉产品的说明

我们给出了交叉乘积理论的两个基本结果的说明。其中之一指出，每当缩减的乘积​​的基础希尔伯特空间表示形式为实时，它的每个正则表示形式都是忠实的$C^{\ast }$-与同构群一起产生相乘积的-代数是忠实的。另一个结果表明，只要它们共同的基本自同构群合适，交叉和完全交叉的乘积就会重合。