Resumen de Algebres à bases bornées

M. Akkar, L. Oubbi, Mohamed Oudadess

• In this paper, we introduce a new class of locally-convex algebras containing the one of unital uniformly $A$-convex algebras. It is the collection of those separated locally-convex algebras which have an algebraic basis whose idempotent hull is bounded. Such algebras are said to be “with $m$- bounded bases”. Under different notions of completeness, we endow these algebras with a complete algebra norm which has the same bounded sets of different kinds. Different questions on the factorization and commutativity are considered.