Abstract :
We first study some properties of A-module homomorphisms ?:X?Y, where X and Y are Fréchet A-modules and A is a unital Fréchet algebra. Then we show that if there exists a continued bisection of the identity for A, then ? is automatically continuous under certain condition on X. In particular, every homomorphism from A into certain Fréchet algebras (including Banach algebra) is automatically continuous. Finally, we show that every unital Fréchet algebra with a continued bisection of the identity, is functionally continuous.
