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

Junge, Marius; Merdy, Christian Le; Xu, Quanhua

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

Authors

Junge, Marius

Merdy, Christian Le

Xu, Quanhua

Description

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.
118 pages