This is an announcement for the paper "$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces" by Marius Junge, Christian Le Merdy and Quanhua Xu.
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.
Archive classification: Functional Analysis
Mathematics Subject Classification: Primary 47A60; Secondary 46L55, 46L69
Remarks: 118 pages
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Submitted from: qx@math.univ-fcomte.fr
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