English

$H^{\infty}$ 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 LpL^p-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and HH^\infty functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, qq-Ornstein-Uhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups.

Keywords

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