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

Christian Le Merdy; Marius Junge; Quanhua Xu

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H^(infty) functional calculus and square functions on noncommutative L^p-spaces

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arxiv math/0601645 v1 pith:GS3JTI52 submitted 2006-01-26 math.FA

H^(infty) functional calculus and square functions on noncommutative L^p-spaces

Marius Junge , Christian Le Merdy , Quanhua Xu This is my paper

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keywords noncommutativesemigroupscalculusfunctionalfunctionsinftysectorialityspaces

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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.

H^(infty) functional calculus and square functions on noncommutative L^p-spaces

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