Closed ideals of finite codimension in regular selfadjoint Banach algebras (Q1823431)

The author gives a generalization of a classic theorem of Gleason-Kahane- Zelazko. He proved in particular that if M is a closed subspace of codimension n in A and if Sp A is \(\sigma\)-compact and every point \(s\in Sp A\) is a \(G_{\delta}\)-set and for any \(x\in M\), \(\hat x(s)=s(x)\), \(s\in Sp A\) has n distinct zeros in Sp A, then there exists n-distinct common zeros of M in Sp A.