On a conjecture concerning some automatic continuity theorems
Résumé
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.
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