| Type de publication : |
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Preprint, Working Paper, Document sans référence, etc. |
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| Domaine : |
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Mathématiques/Analyse fonctionnelle
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| Titre : |
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A sharpened Schwarz-Pick operatorial inequality for nilpotent operators |
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| Auteur(s) : |
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Haykel Gaaya 1 |
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| Laboratoire : |
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| 1 : |
Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX |
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France |
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| Résumé : |
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Let denote by $S(\phi)$ the extremal operator defined by the compression of the unilateral shift $S$ to the model subspace $ H(\phi)=H^{2} \ominus \phi H^{2} $ as the following $S(\phi)f(z)=P(zf(z)),$ where $P$ denotes the orthogonal projection from the Hardy space $H^{2}$ onto $ H(\phi)$ and $\phi$ is an inner function on the unit disc. In this mathematical notes, we give an explicit formula of the numerical radius of the truncated shift $S(\phi)$ in the particular case where $\phi$ is a finite Blaschke product with unique zero and an estimate on the general case. We establish also a sharpened Schwarz-Pick operatorial inequality generalizing a U. Haagerup and P. de la Harpe result for nilpotent operators |
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Langue du texte
intégral : |
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Anglais |
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Date de production,
écriture : |
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17/02/2012 |
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