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Theses

Produits d'opérateurs de Toeplitz sur l'espace de Bergman

Abstract : The subject of this thesis is the study of the product of two Toeplitz operators those defined on the Hardy space of the unit circle as well as those defined on the Bergman space of the unit disc. The two questions raised in my work are as follows :
1) Under which conditions is the product of two Toeplitz operators a Toeplitz operator?
2) Under which conditions is the product of two Toeplitz operators commutative?
For each of these two questions we start by discussing former work along with sevaral technical tools, then we expalin our contibution to this domain. In particular, we give necessary and sufficient conditions for the product of two quasihomogeneous Toeplitz operators to be a Toeplitz operator. Moreover, we chracterize the bounded Toeplitz operators which commute with a quasihomogeneous Toeplitz operator. To motivate this characterization we introduce a new notion-namely the T-root of a quasihomogeneous Toeplitz operator. This work enables us to give an effective construction of a non trivial Toeplitz operator whose powers are all Toeplitz operators.
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https://tel.archives-ouvertes.fr/tel-00011954
Contributor : Issam Louhichi <>
Submitted on : Wednesday, March 15, 2006 - 12:52:57 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Long-term archiving on: : Saturday, April 3, 2010 - 8:58:53 PM

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  • HAL Id : tel-00011954, version 1

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Issam Louhichi. Produits d'opérateurs de Toeplitz sur l'espace de Bergman. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I; Faculté des Sciences de Tunis, 2005. Français. ⟨tel-00011954⟩

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