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| HAL: hal-00672703, version 1 |
| arXiv: 1202.3962 |
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| A sharpened Schwarz-Pick operatorial inequality for nilpotent operators |
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| Haykel Gaaya 1 |
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| (2012-02-17) |
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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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| 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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| Subject | : | Mathematics/Functional Analysis |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1202.3962 |
| hal-00672703, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00672703 | |
| oai:hal.archives-ouvertes.fr:hal-00672703 | |
| From: Haykel Gaaya | |
| Submitted on: Tuesday, 21 February 2012 18:09:24 | |
| Updated on: Tuesday, 21 February 2012 18:09:24 | |
