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

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

2006-01-26

arxiv.org/abs/math/0601645v1

Mathematics

Functional Analysis

118 pages

Scientific paper

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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