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.
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.
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@article{CRMATH_2016__354_11_1087_0, author = {El-Fallah, Omar and El Ibbaoui, Mohamed}, title = {On the singular values of compact composition operators}, journal = {Comptes Rendus. Math\'ematique}, pages = {1087--1091}, publisher = {Elsevier}, volume = {354}, number = {11}, year = {2016}, doi = {10.1016/j.crma.2016.09.012}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.09.012/} }
TY - JOUR AU - El-Fallah, Omar AU - El Ibbaoui, Mohamed TI - On the singular values of compact composition operators JO - Comptes Rendus. Mathématique PY - 2016 SP - 1087 EP - 1091 VL - 354 IS - 11 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.09.012/ DO - 10.1016/j.crma.2016.09.012 LA - en ID - CRMATH_2016__354_11_1087_0 ER -
%0 Journal Article %A El-Fallah, Omar %A El Ibbaoui, Mohamed %T On the singular values of compact composition operators %J Comptes Rendus. Mathématique %D 2016 %P 1087-1091 %V 354 %N 11 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.09.012/ %R 10.1016/j.crma.2016.09.012 %G en %F CRMATH_2016__354_11_1087_0
El-Fallah, Omar; El Ibbaoui, Mohamed. On the singular values of compact composition operators. Comptes Rendus. Mathématique, Tome 354 (2016) no. 11, pp. 1087-1091. doi : 10.1016/j.crma.2016.09.012. http://archive.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”.