The Amenability of Measure Algebras
The Amenability of Measure Algebras
复制标题
测度代数的适用性
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
A. Helemskiĭ
中科院分区：
文献类型：
--
作者：
H. Dales;F. Ghahramani;A. Helemskiĭ
本文证明了局部紧群G的测度代数M（G）服从Banach代数当且仅当G是离散的且服从群。我们的贡献是解决一个猜想，证明M（G）是不服从的情况下，群G是不离散的。事实上，我们将证明一个更强的结果：非离散的局部紧群的测度代数在代数上的某个特征上有一个非零的连续点导子。
In this paper we shall prove that the measure algebra M(G) of a locally compact group G is amenable as a Banach algebra if and only if G is discrete and amenable as a group. Our contribution is to resolve a conjecture by proving that M(G) is not amenable in the case where the group G is not discrete. Indeed, we shall prove a much stronger result: the measure algebra of a non‐discrete, locally compact group has a non‐zero, continuous point derivation at a certain character on the algebra.