Regular spectrum of elements in topological algebras

Abstract

‎‎‎Main properties of the regular (or extended) spectrum of elements in topological algebras (introduced by L‎. ‎Waelbroeck and G‎. ‎R‎. ‎Allan for unital locally convex algebras) are presented‎. ‎Descriptions of the relationship between the usual spectrum and the regular spectrum of elements in topological algebras with jointly continuous multiplication are given‎. ‎It is shown that the usual spectrum and the regular spectrum of elements coincide for Hausdorff locally convex Waelbroeck algebras‎. ‎Main properties of the disolvent map of elements in topological algebras are studied‎.