On a conjecture concerning some automatic continuity theorems

Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let h be an injective homomorphism from A to B. Under additional assumptions, we characterize the continuity of the homomorphism h^(-1) / Im(h) by the fact that the radical (or strong radical) of the closure of Im(h) has only zero as a common point with Im(h). This gives an answer to a conjecture concerning some automatic continuity theorems on uniform topological algebras.Comment: 5 page

A real seminorm with square property is submultiplicative

A seminorm with square property on a real associative algebra is submultiplicativeComment: 3 page

A remark on continuity of positive linear functionals on separable Banach *-algebras

Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R.J.Loy Theorem: Let A be a separable Banach*-algebra with center Z such that ZA has at most countable codimension, then every positive linear functional on A is continuous.Comment: 3 page

On saturated uniformly A-convex algebras

Following ideas of A.C.Cochran, we give a suitable definition of a saturated uniformly A-convex algebra. In the m-convex case, such algebra is a uniform topological one.Comment: 6 page