Geodesic
On the union of sets of semisimplicity
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 2, pp. 256-261 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce the notion of a set of semisimplicity, or $S_3$-set, as a set $\Lambda$ such that if $T$ is a representation of a LCA group $G$ with $Sp(T)\subset\Lambda$, 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 $S$-set is a $S_3$-set. 
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     title = {On the union of sets of semisimplicity},
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     number = {2},
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Gilbert Muraz; Quoc Phong Vu. On the union of sets of semisimplicity. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 2, pp. 256-261. http://geodesic.mathdoc.fr/item/JMAG_2003_10_2_a9/