By using the Furstenberg–Ellis–Namioka structure theorem, we give a decomposition theorem for the Banach algebra $${\mathcal {M}}(G)$$ M ( G ) , i.e. the Banach algebra of those complex regular Borel measures on a compact Hausdorff admissible right topological (or simply CHART) group G for which the natural convolution product makes sense, generalizing an existing result due to Lau and Loy. Next, we characterize the Furstenberg–Ellis–Namioka structure theorem on a family of CHART groups, namely the groups $$E({\mathbb {T}})^{k}$$ E ( T ) k where $$E({\mathbb {T}})$$ E ( T ) is the family of all endomorphisms of the unit circle $${\mathbb {T}}$$ T , and then we apply the generalized decomposition theorem to these groups.

中文翻译：

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关于Lau-Loy 对CHART 群测度代数的分解

通过使用 Furstenberg-Ellis-Namioka 结构定理，我们给出了 Banach 代数 $${\mathcal {M}}(G)$$ M ( G ) 的分解定理，即那些复杂的常规 Borel 测度的 Banach 代数一个紧凑的 Hausdorff 可容许右拓扑（或简称为 CHART）群 G，自然卷积乘积对其有意义，概括了 Lau 和 Loy 的现有结果。接下来，我们在一系列 CHART 群上刻画 Furstenberg-Ellis-Namioka 结构定理，即群 $$E({\mathbb {T}})^{k}$$ E ( T ) k 其中 $$E( {\mathbb {T}})$$ E ( T ) 是单位圆 $${\mathbb {T}}$$ T 的所有自同态族，然后我们将广义分解定理应用于这些群。