A noncommutative martingale convexity inequality
In: Annals of Probability Annals of Probability, Institute of Mathematical Statistics, 2016, 44 (2), pp.867-882. ⟨10.1214/14-AOP990⟩ Annals of Probability, Institute of Mathematical Statistics, 2016, 44 (2), pp.867-882. 〈10.1214/14-AOP990〉 Ann. Probab. 44, no. 2 (2016), 867-882; (2014-05-02)
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Zugriff:
Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful semifinite normal weight $\phi$ and $\mathcal{N}$ be a von Neumann subalgebra of $\mathcal{M}$ such that the restriction of $\phi$ to $\mathcal{N}$ is semifinite and such that $\mathcal{N}$ is invariant by the modular group of $\phi$. Let $\mathcal{E}$ be the weight preserving conditional expectation from $\mathcal{M}$ onto $\mathcal{N}$. We prove the following inequality: \[\|x\|_p^2\ge\bigl \|\mathcal{E}(x)\bigr\|_p^2+(p-1)\bigl\|x-\mathcal{E}(x)\bigr\|_p^2, \qquad x\in L_p(\mathcal{M}),10$ such that for any free group $\mathbb{F}_n$ and any $q\ge4-\varepsilon_0$, \[\|P_t\|_{2\to q}\le1\quad\Leftrightarrow\quad t\ge\log{\sqrt{q-1}},\] where $(P_t)$ is the Poisson semigroup defined by the natural length function of $ \mathbb{F}_n$.
Comment: Published at http://dx.doi.org/10.1214/14-AOP990 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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A noncommutative martingale convexity inequality
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Autor/in / Beteiligte Person: | Xu, Quanhua ; Ricard, Éric ; Laboratoire de Mathématiques Nicolas Oresme (LMNO) ; Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN) ; Normandie Université (NU)-Normandie Université (NU) ; Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB) ; Université de Bourgogne (UB)-Université de Franche-Comté (UFC) ; Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS) ; Laboratoire de Mathématiques Nicolas Oresme ( LMNO ) ; Université de Caen Normandie ( UNICAEN ) ; Normandie Université ( NU ) -Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS ) ; Laboratoire de Mathématiques de Besançon ( LMB ) ; Centre National de la Recherche Scientifique ( CNRS ) -Université de Franche-Comté ( UFC ) |
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Quelle: | Annals of Probability Annals of Probability, Institute of Mathematical Statistics, 2016, 44 (2), pp.867-882. ⟨10.1214/14-AOP990⟩ Annals of Probability, Institute of Mathematical Statistics, 2016, 44 (2), pp.867-882. 〈10.1214/14-AOP990〉 Ann. Probab. 44, no. 2 (2016), 867-882; (2014-05-02) |
Veröffentlichung: | 2014 |
Medientyp: | unknown |
ISSN: | 0091-1798 (print) ; 2168-894X (print) |
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