On a conjecture concerning some automatic continuity theorems |
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Authors: | M. El Azhari |
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Affiliation: | 1. Ecole Normale Supérieure, Avenue Oued Akreuch, Takaddoum, 5118, Rabat, Morocco
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Abstract: | Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let Φ be an injective homomorphism from A to B. Under additional assumptions, we characterize the continuity of the homomorphism Φ?1/Im?Φ by the fact that the radical (or strong radical) of the closure of Im?Φ has only zero as a common point with Im?Φ. This gives an answer to a conjecture concerning some automatic continuity theorems on uniform topological algebras. |
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