Journal of Mathematical Physics, Analysis, Geometry
2003, vol. 10, No 2, pp. 256-261    ( to contents , go back )

On the union of sets of semisimplicity

Gilbert Muraz

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.

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