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Keywords:
locally pseudo-convex algebra; continuous product; $m$-$p$-convexity; Baire space; power maps
locally pseudo-convex algebra; continuous product; $m$-$p$-convexity; Baire space; power maps
Summary:
We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.
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