Continuous characters in weighted algebras (Q1812200)

Let \(X\) be a completely regular Hausdorff space and \(V\) a set of nonnegative (not necessarily upper semicontinuous) functions on \(X\) such that (1) for all \(x\in X\) there is \(v\in V\) such that \(v(x)> 0\); (2) for all \(v_1,v_2\in V\), \(\mu> 0\) there is \(w\in V\) such that \(\max\{\mu v_1,\mu v_2\}\leq w\). Moreover, let \(A\) be a locally convex algebra. The authors first treat the scalar case. They consider certain subalgebras of \(CV(X)\) and show that the corresponding space of continuous characters is homeomorphic to a specific subset of the Stone-Čech-compactification \(\beta X\) of \(X\). Next, they investigate certain subalgebras of \(CV_0(X, A)\) and prove that the continuous characters on such algebras are of the canonical form \(f\mapsto \varphi(f(x))\) with \(x\in X\) and \(\varphi\in M(A)\).