Extended spectral radius in topological algebras (Q1328232)

The authors study the relationships among 8 notions of spectral radius functions \(r_ 1,\dots, r_ 7\) and \(r_ *\) defined for locally convex topological algebras by Zelazko. The functions all coincide for a Banach algebra but need not coincide in the more general setting. The authors summarize the relationships among \(r_ 1,\dots, r_ 7\) and \(r_ *\) and give some new results about their relationship in several classes of locally convex algebras.