$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces

Marius Junge , Christian Le Merdy (1) , Quanhua Xu (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\infty$ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, $q$-Ornstein-Uhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups.

Domaines: Analyse fonctionnelle [math.FA]

Marius Junge, Christian Le Merdy, Quanhua Xu. $H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces. Asterisque, 2006, 305, vi+138 p. ⟨hal-00477043⟩