Applications of the Connes Spectrum to C∗-dynamical systems, III
Applications of the Connes Spectrum to C∗-dynamical systems, III
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Connes 谱在 C* 动力系统中的应用，III
DOI：
10.1016/0022-1236(78)90069-1
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发表时间：
1978
影响因子：
1.7
通讯作者：
G. Pedersen
中科院分区：
文献类型：
--
作者：
Dorte Olesen;G. Pedersen
本文证明了C-代数A与局部紧交换群G的交叉积是素C-代数（任意两个非零理想有非零交）当且仅当满足两个条件：（a）A是G-素的（A的任意两个非零G-不变理想有非零交）;（B）α的Connes谱Γ（α）等于G的整个对偶群.
We show that the crossed product between aC∗-algebraAand a locally compact abelian groupGwith a representation α as automorphisms ofAis a primeC∗-algebra (any two nonzero ideals have a nonzero intersection) if and only if two conditions are satisfied: (a)AisG-prime (any two nonzeroG-invariant ideals ofAhave a nonzero intersection); and (b) the Connes spectrum Γ(α) of α equals the whole dual group ofG.