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Description of quotient algebras in function algebras containing continuous unbounded functions. (English) Zbl 1254.46056

Authors’ abstract: Let \(X\) be a completely regular Hausdorff space, \(\mathfrak{S}\) a cover of \(X\), and \(C_b (X,\mathbb{K};\mathfrak{S})\) the algebra of all \(\mathbb{K}\)-valued continuous functions on \(X\) which are bounded on every \(S \in \mathfrak{S}\). A description of quotient algebras of \(C_b (X,\mathbb{K};\mathfrak{S})\) is given with respect to the topologies of uniform and strict convergence on the elements of \(\mathfrak{S}\).

MSC:

46J10 Banach algebras of continuous functions, function algebras
46J05 General theory of commutative topological algebras
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References:

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