Homogeneous algebras on the circle. I. Ideals of analytic functions

Bennett, Colin; Gilbert, John E.

Annales de l'Institut Fourier, Tome 22 (1972), p. 1-19 / Harvested from Numdam

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Abstract

On désigne par $𝒜$ une algèbre de Banach homogène sur le cercle et par $𝒜^{+}$ la sous-algèbre fermée de $𝒜$ constituée par les fonctions qui ont des prolongements analytiques dans le disque ouvert $D$ . Ce travail considère la structure des idéaux fermés de $𝒜^{+}$ , sous des restrictions convenables sur les propriétés de synthèse de $𝒜$ . En particulier, on caractérise complètement les idéaux fermés de $𝒜^{+}$ tels que les “zero sets” rencontrent le cercle en un ensemble dénombrable. Ces résultats contiennent des résultats précédents de Kahane et de Taylor-Williams obtenus indépendamment.

Let $𝒜$ be a homogeneous algebra on the circle and $𝒜^{+}$ the closed subalgebra of $𝒜$ of functions having analytic extensions into the unit disk $D$ . This paper considers the structure of closed ideals of $𝒜^{+}$ under suitable restrictions on the synthesis properties of $𝒜$ . In particular, completely characterized are the closed ideals in $𝒜^{+}$ whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently.

Publié le : 1972-01-01

MR 49 #3546 | Zbl 0228.46046 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.422

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     author = {Bennett, Colin and Gilbert, John E.},
     title = {Homogeneous algebras on the circle. I. Ideals of analytic functions},
     journal = {Annales de l'Institut Fourier},
     volume = {22},
     year = {1972},
     pages = {1-19},
     doi = {10.5802/aif.422},
     mrnumber = {49 \#3546},
     zbl = {0228.46046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1972__22_3_1_0}
}

Bennett, Colin; Gilbert, John E. Homogeneous algebras on the circle. I. Ideals of analytic functions. Annales de l'Institut Fourier, Tome 22 (1972) pp. 1-19. doi : 10.5802/aif.422. http://gdmltest.u-ga.fr/item/AIF_1972__22_3_1_0/

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