A note on irreducible representations of some vector-valued function algebras

Abstract

‎Let $\pi‎ :‎\mathcal{E}$ $\rightarrow X$ be a bundle of Banach algebras‎, ‎where $X$ is a completely regular Hausdorff space‎. ‎We identify the sets of irreducible representations of several topological subalgebras of $\Gamma(\pi ),$ the space of continuous sections of $\pi‎ .‎$ The results unify recent and older work of various authors regarding representations on algebra-valued function spaces‎.