H^∞ functional calculus and square functions on noncommutative L^p-spaces

2006/01/26 by Marius Junge, Junge, Marius, Christian Le Merdy +3 · 1 citation
Mathematics · #46L69 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A60 #Secondary 46L55 #math.FA #msc:46L55 #msc:46L69 #msc:47A60

paper · pdf · doi:10.48550/arxiv.math/0601645

118 pages

arxiv created 2006/01/26 · arxiv updated 2009/12/01

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^∞ 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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• Square functions for Ritt operators on noncommutative L^p-spaces

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