no. 4
Theorems of Korovkin type for adapted spaces
Annales de l'Institut Fourier, Tome 23 (1973) no. 4, pp. 245-260.

On montre que les méthodes développées dans un travail antérieur de l’auteur sur le problème de Dirichlet pour la frontière de Silov [Annales Inst. Fourier, 11 (1961)] permettent de retrouver d’une manière nouvelle et naturelle les résultats les plus importants sur la convergence d’opérateurs positifs linéaires dans les espaces de fonctions continues sur un espace compact.

La notion d’un espace adapté de fonctions continues, introduite par Choquet, en liaison avec des résultats de Mokobodzki-Sibony permettent une extension au cas des espaces localement compacts. En particulier, le problème d’une caractérisation de la fermeture de Korovkin d’un espace adapté est résolu.

It is shown that the methods developed in an earlier paper of the author about a Dirichlet problem for the Silov boundary [Annales Inst. Fourier, 11 (1961)] lead in a new and natural way to the most important results about the convergence of positive linear operators on spaces of continuous functions defined on a compact space. Choquet’s notion of an adapted space of continuous functions in connection with results of Mokobodzki-Sibony opens the possibility of extending these results to the case of locally compact spaces. In particular, the so-called Korovkin closure of an adapted space is characterized.

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     title = {Theorems of {Korovkin} type for adapted spaces},
     journal = {Annales de l'Institut Fourier},
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Bauer, Heinz. Theorems of Korovkin type for adapted spaces. Annales de l'Institut Fourier, Tome 23 (1973) no. 4, pp. 245-260. doi : 10.5802/aif.490. https://aif.centre-mersenne.org/articles/10.5802/aif.490/

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