Module homomorphisms from Frechet algebras
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Abstract:
We first study some properties of $A$-module homomorphisms $theta:Xrightarrow Y$, 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.
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Journal title
volume 43 issue 2
pages 455- 466
publication date 2017-04-01
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