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A characterisation of a certain class of convolution algebras

Published online by Cambridge University Press:  20 January 2009

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In (6) Taylor has introduced the notion of a convolution measure algebra. In the same paper he constructed a canonical embedding of an arbitrary, semisimple commutative convolution measure algebra A into the algebra M(S) of all bounded, regular Borel measures on a compact semigroup S. This embedding has the properties that A is σ(M(S), C(S)-dense in M(S), that if μ is in A and ν is absolutely continuous with respect to μ, then ν is in A and that the set A^ of non-zero complex homomorphisms of A can be identified with the set S^ of continuous semicharacters of S where hA^ is identified with χ ∈ S^ by the equation

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Research Article
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Copyright © Edinburgh Mathematical Society 1973