Let be a homogeneous algebra on the circle and the closed subalgebra of of functions having analytic extensions into the unit disk . This paper considers the structure of closed ideals of under suitable restrictions on the synthesis properties of . In particular, completely characterized are the closed ideals in 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.
On désigne par une algèbre de Banach homogène sur le cercle et par la sous-algèbre fermée de constituée par les fonctions qui ont des prolongements analytiques dans le disque ouvert . Ce travail considère la structure des idéaux fermés de , sous des restrictions convenables sur les propriétés de synthèse de . En particulier, on caractérise complètement les idéaux fermés de 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.
@article{AIF_1972__22_3_1_0, 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}, mrnumber = {49 #3546}, zbl = {0228.46046}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.422/} }
TY - JOUR AU - Bennett, Colin AU - Gilbert, John E. TI - Homogeneous algebras on the circle. I. Ideals of analytic functions JO - Annales de l'Institut Fourier PY - 1972 SP - 1 EP - 19 VL - 22 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.422/ DO - 10.5802/aif.422 LA - en ID - AIF_1972__22_3_1_0 ER -
%0 Journal Article %A Bennett, Colin %A Gilbert, John E. %T Homogeneous algebras on the circle. I. Ideals of analytic functions %J Annales de l'Institut Fourier %D 1972 %P 1-19 %V 22 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.422/ %R 10.5802/aif.422 %G en %F 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, Volume 22 (1972) no. 3, pp. 1-19. doi : 10.5802/aif.422. http://www.numdam.org/articles/10.5802/aif.422/
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