The three space problem for locally pseudoconvex algebras

Abstract

The three space problem for locally pseudoconvex algebras is considered in this paper. It is shown that a locally pseudoconvex algebra E, with jointly continuous multiplication, is locally m-pseudoconvex, if E contains a two-sided ideal I such that I (in the subset topology) and E / I (in the quotient topology) are locally m-pseudoconvex algebras.