The strong dual of measure algebras with certain locally convex topologies

For a locally compact group G, we introduce and study a class of locally convex topologies T on the measure algebra M(G) of G. In particular, we show that the strong dual of (M(G); T) can be identified with a closed subspace of the Banach space M(G)*; we also investigate some properties of the locally convex space (M(G); T). Finally, we show that the spectrum of (M(G); T) is discrete and nonempty if and only if G is finite. 10.1017/S000497271300014