A noncommutative martingale convexity inequality

• Ricard, Éric ^[2] ; Xu, Quanhua ^[1]
  1. [1] Wuhan University

     Wuhan University

     China

     
  2. [2] Université de Caen Basse-Normandie
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 2, 2016, págs. 867-882
• Idioma: inglés
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• Resumen

  • Let M be a von Neumann algebra equipped with a faithful semifinite normal weight ϕ and N be a von Neumann subalgebra of M such that the restriction of ϕ to N is semifinite and such that N is invariant by the modular group of ϕ. Let E be the weight preserving conditional expectation from M onto N. As an application we show that there exists ε0>0 such that for any free group Fn and any q≥4−ε0, ∥Pt∥2→q≤1⇔t≥logq−1−−−−√, where (Pt) is the Poisson semigroup defined by the natural length function of Fn.