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

Document Type: Original Article


1 Wilkes Honors College Florida Atlantic University, ‎Estonia

2 Trinity College, USA


‎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.