no. 4
The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition
Annales de l'Institut Fourier, Tome 26 (1976) no. 4, pp. 207-237.

Nous prouvons que le problème de Levi pour certains espaces localement convexes et séparés E sur C admettant une décomposition de Schauder de dimension finie (par exemple pour les espaces de Fréchet ou de Silva avec une base de Schauder) a une solution, c’est-à-dire tout domaine pseudo-convexe étalé sur E est un domaine d’existence d’une fonction analytique. Nous démontrons également qu’un domaine pseudoconvexe étalé sur un espace de Fréchet ou de Silva avec une décomposition de Schauder de dimension finie est holomorphiquement convexe et satisfait à un théorème d’approximation du type d’Oka-Weil.

It is proved that the Levi problem for certain locally convex Hausdorff spaces E over C with a finite dimensional Schauder decomposition (for example for Fréchet or Silva spaces with a Schauder basis) the Levi problem has a solution, i.e. every pseudoconvex domain spread over E is a domain of existence of an analytic function. It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex and satisfies an approximation theorem of the Oka-Weil type.

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     author = {Schottenloher, Martin},
     title = {The {Levi} problem for domains spread over locally convex spaces with a finite dimensional {Schauder} decomposition},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Imprimerie Durand},
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     volume = {26},
     number = {4},
     year = {1976},
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Schottenloher, Martin. The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition. Annales de l'Institut Fourier, Tome 26 (1976) no. 4, pp. 207-237. doi : 10.5802/aif.638. https://aif.centre-mersenne.org/articles/10.5802/aif.638/

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