Analytic semigroups on vector valued noncommutative $L^p$-spaces
Volume 216 / 2013
Studia Mathematica 216 (2013), 271-290
MSC: 46L51, 46L07, 47D03.
DOI: 10.4064/sm216-3-5
Abstract
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.
