The local structure of some measure-algebra homomorphisms (Q1824803)

Extending classical theorems, we obtain representations for bounded linear transformations from L-spaces to Banach spaces with a separable predual. In the case of homomorphisms from a convolution measure algebra to a Banach algebra, we obtain a generalization of Šreĭder's representation of the Gelfand spectrum via generalized characters. The homomorphisms from the measure algebra on a LCA group, G, to that on the circle are analyzed in detail. If the torsion subgroup of G is denumerable, one consequence is the following necessary and sufficient condition that a positive finite Borel measure on G be continuous: \(\exists \gamma_{\alpha}\to \infty\) in \(\hat G\) such that \(\forall n\neq 0\) \({\hat \mu}\)(\(\gamma^ n_{\alpha})\to 0\).