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

Cyril Agrafeuil

Studia Mathematica (2005)

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

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 ω ( n ) = ( 1 + n ) s (n ≥ 0) and the sequence ( ω ( - n ) / ( 1 + n ) s ) n ≥ 0 is non-decreasing. We define the Banach algebra A ω ( ) = f ∈ ( ) : | | f | | ω = ∑ n = - ∞ + ∞ | f ̂ ( n ) | ω ( n ) < + ∞ . If I is a closed ideal of A ω ( ) , we set h ⁰ ( I ) = z ∈ : f ( z ) = 0 ( f ∈ I ) . We describe all closed ideals I of A ω ( ) such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra A ⁺ s ( ) = f ∈ A ω ( ) : f ̂ ( n ) = 0 ( n < 0 ) without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating sets for ∞ , 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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