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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107708In 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.118 pagesFunctional AnalysisPrimary 47A60; Secondary 46L55, 46L69$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spacestext