no. 9
Mathematical analysis/Functional analysis
On the representation by sums of algebras of continuous functions
[Sur la représentation des algèbres de fonctions continues comme sommes de sous-algèbres]

Présenté par : the Editorial Board

Asgarova, Aida Kh.1 ; Ismailov, Vugar E.1
1 Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Az-1141, Baku, Azerbaijan
Comptes Rendus. Mathématique, Tome 355 (2017) no. 9, pp. 949-955.

Nous donnons une condition nécessaire pour la représentation d'un espace de fonctions continues comme la somme d'un nombre fini k de ses sous-algèbres fermées. Une condition suffisante pour ce problème a été obtenue par Sternfeld en 1978. Dans le cas de deux sous-algèbres (k=2), notre condition nécessaire se trouve être également suffisante. Dans le cas d'une seule sous-algèbre (k=1), notre résultat coïncide avec une version du théorème de Stone–Weierstrass classique.

We give a necessary condition for the representation of the space of continuous functions by sums of its k closed subalgebras. A sufficient condition for this representation problem was first obtained by Sternfeld in 1978. In case of two subalgebras (k=2), our necessary condition turns out to be also sufficient. If k=1, our result coincides with a version of the classical Stone–Weierstrass theorem.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.015
Asgarova, Aida Kh. 1 ; Ismailov, Vugar E. 1

1 Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Az-1141, Baku, Azerbaijan 
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Asgarova, Aida Kh.; Ismailov, Vugar E. On the representation by sums of algebras of continuous functions. Comptes Rendus. Mathématique, Tome 355 (2017) no. 9, pp. 949-955. doi : 10.1016/j.crma.2017.09.015. http://www.numdam.org/articles/10.1016/j.crma.2017.09.015/

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