Analytic semigroups on vector valued noncommutative $L^p$-spaces

Volume 216 / 2013

Cédric Arhancet Studia Mathematica 216 (2013), 271-290 MSC: 46L51, 46L07, 47D03. DOI: 10.4064/sm216-3-5


We give sufficient conditions on an operator space $E$ and on a semigroup of operators on a von Neumann algebra $M$ to obtain a bounded analytic or $R$-analytic semigroup $(T_t \otimes \mathrm {Id}_E)_{t \geq 0}$ on the vector valued noncommutative $L^p$-space $L^p(M,E)$. Moreover, we give applications to the $H^\infty (\varSigma _\theta )$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.


  • Cédric ArhancetLaboratoire de Mathématiques
    Universitéde Franche-Comté
    25 030 Besançon Cedex, France

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