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

Marius Junge·Christian Le Merdy·Quanhua Xu
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Abstract

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.

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Marius Junge, Christian Le Merdy, Quanhua Xu. 2006-01-26. $H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces. https://arxiv.org/abs/math/0601645

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