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Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ZARRABI, Mohamed | |
| dc.contributor.author | AGRAFEUIL, Cyril | |
| dc.date.accessioned | 2024-04-04T02:51:52Z | |
| dc.date.available | 2024-04-04T02:51:52Z | |
| dc.date.issued | 2008 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192010 | |
| dc.description.abstractEn | We denote by $\bbt$ the unit circle and by $\bbd$ the unit disc. Let $\calb$ be a semi-simple unital commutative Banach algebra of functions holomorphic in $\bbd$ and continuous on $\overline{\bbd}$, endowed with the pointwise product. We assume that $\calb$ is continously imbedded in the disc algebra and satisfies the following conditions: \\ (H1) The space of polynomials is a dense subset of $\calb$. \\ (H2) $\lim_{n\to +\infty}\|z^n\|_{\calb}^{1/ n}=1$.\\ (H3) There exist $k \geq 0$ and $C > 0$ such that \begin{eqnarray*} \big| 1- |\lambda| \big|^{k} \big\| f \big\|_{\calb} \leq C \big\| (z-\lambda) f \big\|_{\calb}, \quad (f \in \calb, |\lambda| < 2) \end{eqnarray*} When $\calb$ satisfies in addition the analytic Ditkin condition, we give a complete characterisation of closed ideals $I$ of $\calb$ with countable hull $h(I)$, where $$ h(I) = \big\{ z \in \overline{\bbd} : \, f(z) = 0, \quad (f \in I) \big\}. $$ Then, we apply this result to many algebras for which the structure of all closed ideals is unknown. We consider, in particular, the weighted algebras $\ell^1(\omega$) and $L^1(\bbr^{+},\omega)$. | |
| dc.language.iso | en | |
| dc.subject.en | Ditkin Condition | |
| dc.subject.en | Closed ideals | |
| dc.subject.en | Banach algebras | |
| dc.subject.en | Ditkin Condition. | |
| dc.title.en | Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary. | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Publicacions Matemàtiques | |
| bordeaux.page | 19-56 | |
| bordeaux.volume | 52 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00288497 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00288497v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Publicacions%20Matem%C3%A0tiques&rft.date=2008&rft.volume=52&rft.spage=19-56&rft.epage=19-56&rft.au=ZARRABI,%20Mohamed&AGRAFEUIL,%20Cyril&rft.genre=article |
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