# Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Studia Mathematica (2005)

• Volume: 167, Issue: 2, page 133-151
• ISSN: 0039-3223

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## Abstract

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We denote by the unit circle and by the unit disc of ℂ. Let s be a non-negative real and ω a weight such that $\omega \left(n\right)={\left(1+n\right)}^{s}$ (n ≥ 0) and the sequence ${\left(\omega \left(-n\right)/{\left(1+n\right)}^{s}\right)}_{n\ge 0}$ is non-decreasing. We define the Banach algebra ${A}_{\omega }\left(\right)={f\in \left(\right):||f||}_{\omega }={\sum }_{n=-\infty }^{+\infty }|f̂\left(n\right)|\omega \left(n\right)<+\infty$. If I is a closed ideal of ${A}_{\omega }\left(\right)$, we set $h⁰\left(I\right)=z\in :f\left(z\right)=0\left(f\in I\right)$. We describe all closed ideals I of ${A}_{\omega }\left(\right)$ such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra $A{⁺}_{s}\left(\right)=f\in {A}_{\omega }\left(\right):f̂\left(n\right)=0\left(n<0\right)$ without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating sets for ${}^{\infty }$, the space of infinitely differentiable functions in the closed unit disc ̅ and holomorphic in .

## How to cite

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Cyril Agrafeuil. "Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable." Studia Mathematica 167.2 (2005): 133-151. <http://eudml.org/doc/284392>.

@article{CyrilAgrafeuil2005,
author = {Cyril Agrafeuil},
journal = {Studia Mathematica},
keywords = {Beurling algebra; closed ideal; power bounded operator; interpolation set; countable spectrum},
language = {fre},
number = {2},
pages = {133-151},
title = {Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable},
url = {http://eudml.org/doc/284392},
volume = {167},
year = {2005},
}

TY - JOUR
AU - Cyril Agrafeuil
TI - Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable
JO - Studia Mathematica
PY - 2005
VL - 167
IS - 2
SP - 133
EP - 151
LA - fre
KW - Beurling algebra; closed ideal; power bounded operator; interpolation set; countable spectrum
UR - http://eudml.org/doc/284392
ER -

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