$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces
Functional Analysis
2007-05-23 v1
Abstract
In this work we investigate semigroups of operators acting on noncommutative -spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, -Ornstein-Uhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups.
Cite
@article{arxiv.math/0601645,
title = {$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces},
author = {Marius Junge and Christian Le Merdy and Quanhua Xu},
journal= {arXiv preprint arXiv:math/0601645},
year = {2007}
}
Comments
118 pages