Functional analysis
On the singular values of compact composition operators
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1087-1091.

Let μ be a positive Borel measure on the unit disc and let Tμ 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 h(Tμ). As consequence, we give some asymptotic estimates of eigenvalues of Tμ. We also apply these results to composition operators and give some concrete examples.

Soit μ une mesure de Borel positive sur le disque unité et soit Tμ 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 h(Tμ). Ceci nous permet d'obtenir quelques estimations asymptotiques des valeurs propres de Tμ. Nous appliquons ces résultats pour les opérateurs de composition et donnons ensuite quelques exemples concrets.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.09.012
El-Fallah, Omar 1; El Ibbaoui, Mohamed 1

1 Laboratoire Analyse et Applications – URAC/03, Mohammed V University in Rabat, B.P. 1014, Rabat, Morocco
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El-Fallah, Omar; El Ibbaoui, Mohamed. On the singular values of compact composition operators. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1087-1091. doi : 10.1016/j.crma.2016.09.012. http://www.numdam.org/articles/10.1016/j.crma.2016.09.012/

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