On the union of sets of semisimplicity
Institut Fourier, B.P. 74 38402 Saint-Martin-d`Heres Cedex, France
Quoc Phong Vu
Department of Mathematics, Ohio University 321 Morton Hall Athens, OH 45701, USA
Received January 17, 2003
Communicated by G.M. Feldman
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 Sp(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.