On a conjecture concerning some automatic continuity theorems

Mohammed El Azhari (1)

1 UM5 - Université Mohammed V de Rabat [Agdal]

Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let Ф be an injective homomorphism from A to B. Under additional assumptions, we characterize the continuity of the homomorphism Ф-1 / ImФ by the fact that the radical (or strong radical) of the closure of ImФ has only zero as a common point with ImФ. This gives an answer to a conjecture concerning some automatic continuity theorems on uniform topological algebras.

Mots clés: Uniform topological algebra; continuity of homomorphism; weakly regular algebra

Domaines: Analyse fonctionnelle [math.FA]

Mohammed El Azhari. On a conjecture concerning some automatic continuity theorems. Rendiconti del Circolo Matematico di Palermo, 2012, 61 (1), pp.13-17. ⟨10.1007/s12215-011-0070-2⟩. ⟨hal-01303274⟩