On the representation by sums of algebras of continuous functions

Aida Kh. Asgarova; Vugar E. Ismailov

doi:10.1016/j.crma.2017.09.015

Mathematical analysis/Functional analysis

On the representation by sums of algebras of continuous functions

Presented by: the Editorial Board

Aida Kh. Asgarova ¹; Vugar E. Ismailov ¹

¹ Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Az-1141, Baku, Azerbaijan

Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 949-955.

Abstract
Résumé

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.

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.

Received: 2016-05-29
Accepted: 2017-09-20
Published online: 2017-09-01

DOI: 10.1016/j.crma.2017.09.015

Author's affiliations:

Aida Kh. Asgarova ¹; Vugar E. Ismailov ¹

¹ Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Az-1141, Baku, Azerbaijan

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Aida Kh. Asgarova; Vugar E. Ismailov. On the representation by sums of algebras of continuous functions. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 949-955. doi : 10.1016/j.crma.2017.09.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.015/

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