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
E-mail: Gilbert.Muraz@ujf-grenoble.fr

Quoc Phong Vu

Department of Mathematics, Ohio University 321 Morton Hall Athens, OH 45701, USA
E-mail: qvu@bing.math.ohiou.edu

Received January 17, 2003

Communicated by G.M. Feldman

Abstract

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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