On the union of sets of semisimplicity

Анотація

We introduce the notion of a set of semisimplicity, or S₃-set, as a set L such that if T is a representation of a LCA group G with S_p(T) Ì L, then T generates a semisimple Banach algebra. We prove that the union of S₃-sets is a S₃-set, provided their intersection is countable. In particular, the union of a countable set and a Helson S-set is a S₃-set.