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arXiv · 1211.3426

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

Cédric Arhancet
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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 a $R$-analytic semigroup $(T_t \otimes Id_E)_{t \geq 0}$ on the vector valued noncommutative $L^p$-space $L^p(M,E)$. Moreover, we give applications to the $H^\infty(\Sigma_\theta)$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

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Cédric Arhancet. 2012-11-14. Analytic semigroups on vector valued noncommutative $L^p$-spaces. https://arxiv.org/abs/1211.3426

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