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On the ideal structure of algebras of LMC-algebra valued functions. (English) Zbl 0812.46045

Summary: Let \(X\) be a completely regular topological space and \(A\) a commutative locally \(m\)-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra \(C(X,A)\) (\(=\) all continuous \(A\)-valued functions defined on \(X\)). The topology on \(C(X,A)\) is defined by a certain family of seminorms. The compact-open topology of \(C(X,A)\) is a special case of this topology.

MSC:

46J05 General theory of commutative topological algebras
46J20 Ideals, maximal ideals, boundaries
46E40 Spaces of vector- and operator-valued functions
46H05 General theory of topological algebras
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