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Structure theory for a class of convolution algebras of vector-valued measures. (English) Zbl 0706.43002

Let S be a totally ordered compact topological semigroup, the topology on S being defined in terms of ordering. Let M(S,X) denote convolution algebra of vector-valued measures on S with values in Banach algebra X. It is shown that M(S,X) is a commutative Banach algebra. The maximal ideal space of M(S,X) is identified. If X is semi-simple then so is M(S,X).
Reviewer: H.L.Vasudeva

MSC:

43A10 Measure algebras on groups, semigroups, etc.
46E40 Spaces of vector- and operator-valued functions
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