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An example of a Fréchet algebra which is a principal ideal domain

Graciela Carboni; Angel Larotonda — 2000

Studia Mathematica

We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.

A characterization of holomorphic germs on compact perfect sets

Graciela Carboni; Angel Rafael Larotonda — 2004

Commentationes Mathematicae Universitatis Carolinae

Let $K \subseteq ℂ$ be a perfect compact set, $E$ a quasi-complete locally convex space over $ℂ$ and $f : K \to E$ a map. In this note we give a necessary and sufficient condition — in terms of differential quotients — for $f$ to have a holomorphic extension on a neighborhood of $K$ .

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