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Keywords:
strict topologies; locally convex algebras; locally $m$-convex algebras
strict topologies; locally convex algebras; locally $m$-convex algebras
Summary:
Let $X$ be a completely regular Hausdorff space, $C_{b}(X)$ the space of all scalar-valued bounded continuous functions on $X$ with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally $m$-convex.
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