On uniform topological algebras

Mohammed El Azhari (1)

1 UM5 - Université Mohammed V de Rabat [Agdal]

The uniform norm on a uniform normed Q-algebra is the only uniform Q-algebra norm on it. The uniform norm on a regular uniform normed Q-algebra with unit is the only uniform norm on it. Let A be a uniform topological algebra whose spectrum M(A) is equicontinuous, then A is a uniform normed algebra. Let A be a regular semisimple commutative Banach algebra, then every algebra norm on A is a Q-algebra norm on A.

Mots clés: Uniform topological algebra; regular algebra; uniform seminorm

Domaines: Analyse fonctionnelle [math.FA]

Mohammed El Azhari. On uniform topological algebras. Analele Stiintifice Ale Universitatii "Al. I. Cuza" Din Iasi Matematica, 2017, 63 (1), pp.177-180. ⟨hal-01306458⟩