Module homomorphisms from Frechet algebras

Document Type : Research Paper


Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Shahrekord‎, ‎P.O‎. ‎Box 88186-34141‎, ‎Shahrekord‎, ‎Iran.


We first study some properties‎ ‎of $A$-module homomorphisms $\theta:X\rightarrow Y$‎, ‎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 $\theta$ 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.


Main Subjects

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