On the union of sets of semisimplicityGilbert Muraz Institut Fourier, B.P. 74 38402 SaintMartind`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 Abstract We introduce the notion of a set of semisimplicity, or S_{3}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 S_{3}sets is a S_{3}set, provided their intersection is countable. In particular, the union of a countable set and a Helson Sset is a S_{3}set.
