Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 2, pp. 256-261
Citer cet article
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/
@article{JMAG_2003_10_2_a9,
author = {Gilbert Muraz and Quoc Phong Vu},
title = {On the union of sets of semisimplicity},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {256--261},
year = {2003},
volume = {10},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_2_a9/}
}
TY - JOUR
AU - Gilbert Muraz
AU - Quoc Phong Vu
TI - On the union of sets of semisimplicity
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2003
SP - 256
EP - 261
VL - 10
IS - 2
UR - http://geodesic.mathdoc.fr/item/JMAG_2003_10_2_a9/
LA - en
ID - JMAG_2003_10_2_a9
ER -
%0 Journal Article
%A Gilbert Muraz
%A Quoc Phong Vu
%T On the union of sets of semisimplicity
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2003
%P 256-261
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/JMAG_2003_10_2_a9/
%G en
%F JMAG_2003_10_2_a9
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.
