CONTINUITY ON A CLASS OF F-ALGEBRAS

Abstract

In the first part of the paper, we give some criteria of continuity of the spectral radius functions on strongly sequential $\mathrm{\Sigma }$-fundamental $F$-algebras. Several examples of spectral continuity are discussed as well. The second part uses the results of the first part to investigate the automatic continuity of linear mappings and homomorphisms on a class of $F$-algebras.