A. El Kinani
Equicontinuity of power maps in locally pseudo-convex algebras

Comment.Math.Univ.Carolinae 44,1 (2003) 91-98.

Abstract: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.

Keywords: locally pseudo-convex algebra, continuous product, $m$-$p$-convexity, Baire space, power maps
AMS Subject Classification: Primary 46H05