Automatic Continuity of Dense Range Homomorphisms into Multiplicatively Semisimple Complete Normed Algebras

The following open problem state that: If  is a dense range homomorphism from Banach algebra into Banach algebra  such that  is semisimple. Is  automatically continuous? (see[1])<br /> In [5] given a partial solution of the above problem as follows:<br /> Let and  be a Fréchet algebras...

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