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

By Marius Junge, Christian Le Merdy, Quanhua Xu. Astérisque, 2006

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b34a2b14347de5193df42d8b4beac19ee2abbc9a