Characters on certain function algebras. (English) Zbl 0932.46041

Authors’ summary: The main result of this note is a characterization of all (not necessarily continuous) multiplicative linear functionals on the algebra \(C(X,A)\) of continuous functions from a real-compact topological space \(X\) to a metrizable topological algebra \(A\). This complements known results for \(Q\)-algebras due to Hery. For compact spaces \(X\) the requirement on \(A\) can be weakened. Finally, a description of all characters on the topological algebra \(H(\Omega, A)\) of algebra-valued holomorphic functions on an open subset \(\Omega\) is given.


46J10 Banach algebras of continuous functions, function algebras
46H05 General theory of topological algebras
46E40 Spaces of vector- and operator-valued functions