Functional continuity of unital $B_{0}$-algebras with orthogonal bases

Mohammed El Azhari (1)

1 UM5 - Université Mohammed V de Rabat [Agdal]

Let $A$ be a unital $B_{0}$-algebra with an orthogonal basis, then every multiplicative linear functional on $A$ is continuous. This gives an answer to a problem posed by Z. Sawon and Z. Wronski.

Mots clés: multiplicative linear functional; orthogonal basis; $B_{0}$-algebra

Domaines: Analyse fonctionnelle [math.FA]

Mohammed El Azhari. Functional continuity of unital $B_{0}$-algebras with orthogonal bases. Le Matematiche, 2017, 72 (1), pp.97-102. ⟨hal-01205148v3⟩