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Theses

Titre : Inégalités de martingales non commutatives et Applications

Abstract : This thesis presents some results of the theory of noncommutative probability. It deals in particular with martingale inequalities in von Neumann algebras, and their associated Hardy spaces. The first part proves a noncommutative analogue of the Davis decomposition, involving the square function. The usual arguments using stopping times in the commutative case are no longer valid in this setting, and the proof is based on a dual approach. The second main result of this part determines the dual of the conditioned Hardy space h_1(M). These results are then extended to the case 1
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Mathilde Perrin. Titre : Inégalités de martingales non commutatives et Applications. Mathématiques générales [math.GM]. Université de Franche-Comté, 2011. Français. ⟨NNT : 2011BESA2023⟩. ⟨tel-00839544⟩

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