We characterize the ideals of the semicrossed product $C_0(X)\times _\phi {\mathbb Z}_+$, associated with suitable sequences of closed subsets of X, with left (resp. right) approximate unit. As a consequence, we obtain a complete characterization of ideals with left (resp. right) approximate unit under the assumptions that X is metrizable and the dynamical system $(X,\phi )$ contains no periodic points.

中文翻译：

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半交叉积中具有近似单位的理想

我们描述半交叉乘积$C_0(X)\times _\phi {\mathbb Z}_+$的理想，与X的闭合子集的合适序列相关，具有左（或右）近似单位。因此，在X可度量且动力系统$(X,\phi )$不包含周期点的假设下，我们获得了具有左（或右）近似单位的理想的完整表征。