## 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.

### MSC:

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