Description of all closed maximal regular ideals in subalgebras of the algebra \(C(X;A;\sigma)\). (English) Zbl 1054.46030

Arizmendi, Hugo (ed.) et al., Topological algebras and their applications. Proceedings of the 4th international conference, Oaxaca, Mexico, July 1–5, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3556-4/pbk). Contemp. Math. 341, 1-15 (2004).
Let \(X\) be a completely regular Hausdorff space, \(\sigma\) a compact cover of \(X\), closed with respect to finite unions. Let \(A\) be a locally \(m\)-pseudoconvex Hausdorff algebra, a locally pseudoconvex Waelbroeck Hausdorff algebra or an exponentially galbed Hausdorff algebra with bounded elements. Let \(C(X,A;\sigma)\) be the algebra of all continuous \(A\)-valued functions on \(X\), endowed the topology of \(\sigma\)-convergence. The main result in this paper is a description of closed maximal regular one-sided and two-sided ideals in subalgebras of \(C(X,A;\sigma)\).
For the entire collection see [Zbl 1031.46002].


46H10 Ideals and subalgebras
46H05 General theory of topological algebras
46H20 Structure, classification of topological algebras