Locally pseudoconvex inductive limit of sequences of locally pseudoconvex algebras

Abstract

Conditions such that a locally $k$-convex inductive limit of a sequence of $k_n$-normed algebras is a locally $m$-($k$-convex) algebra, are given. It is shown that every locally pseudoconvex inductive limit $E$ of a sequence of commutative locally $m$-pseudoconvex algebras is a commutative locally\break $m$-pseudoconvex algebra if the multiplication in $E$ is jointly continuous.