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

Cédric Arhancet

Analytic semigroups on vector valued noncommutative

L^{p}

-spaces

Cédric Arhancet

Studia Mathematica, Tome 215 (2013), p. 271-290 / Harvested from The Polish Digital Mathematics Library

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Résumé

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 ( ${(T \otimes I d_{E})}_{t \geq 0}$ on the vector valued noncommutative $L^{p}$ -space $L^{p} (M, E)$ . Moreover, we give applications to the $H^{\infty} (Σ_{θ})$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

Publié le : 2013-01-01

Zbl 1283.46044

EUDML-ID : urn:eudml:doc:286467

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Cédric Arhancet. Analytic semigroups on vector valued noncommutative $L^{p}$-spaces. Studia Mathematica, Tome 215 (2013) pp. 271-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-5/