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Comptes Rendus Mathématique
Volume 354, n° 11
pages 1087-1091 (novembre 2016)
Doi : 10.1016/j.crma.2016.09.012
Received : 11 May 2016 ;  accepted : 26 September 2016
On the singular values of compact composition operators
Sur les valeurs singulières des opérateurs de composition compacts
 

Omar El-Fallah , Mohamed El Ibbaoui
 Laboratoire Analyse et Applications – URAC/03, Mohammed V University in Rabat, B.P. 1014, Rabat, Morocco 

Abstract

Let μ be a positive Borel measure on the unit disc and let   be the associated Toeplitz operator on a standard Bergman space. Under some convexity conditions on a positive function h , we give an upper and lower bounds of the trace of  . As consequence, we give some asymptotic estimates of eigenvalues of  . We also apply these results to composition operators and give some concrete examples.

The full text of this article is available in PDF format.
Résumé

Soit μ une mesure de Borel positive sur le disque unité et soit   l'opérateur de Toeplitz associé à μ sur un espace de Bergman standard. Pour une fonction positive h satisfaisant des conditions de convexité, nous donnons des bornes inférieures et supérieures de la trace de  . Ceci nous permet d'obtenir quelques estimations asymptotiques des valeurs propres de  . Nous appliquons ces résultats pour les opérateurs de composition et donnons ensuite quelques exemples concrets.

The full text of this article is available in PDF format.

 Research partially supported by “Hassan II Academy of Science and Technology”.



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