no. 3
Homogeneous algebras on the circle. I. Ideals of analytic functions
Annales de l'Institut Fourier, Tome 22 (1972) no. 3, pp. 1-19.

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.

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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},
     pages = {1--19},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {22},
     number = {3},
     year = {1972},
     doi = {10.5802/aif.422},
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Bennett, Colin; Gilbert, John E. Homogeneous algebras on the circle. I. Ideals of analytic functions. Annales de l'Institut Fourier, Tome 22 (1972) no. 3, pp. 1-19. doi : 10.5802/aif.422. https://aif.centre-mersenne.org/articles/10.5802/aif.422/

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