Comptes Rendus
Functional analysis
Fréchet differentiability of the norm of Lp-spaces associated with arbitrary von Neumann algebras
[Différentiabilité au sens de Fréchet de la norme d'un espace Lp associé à une algèbre de von Neumann arbitraire]
Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 923-927.

Let M be a von Neumann algebra and let (Lp(M),p), 1p< be Haagerup's Lp-space on M. We prove that the differentiability properties of p are precisely the same as those of classical (commutative) Lp-spaces. Our main instruments are multiple operator integrals and singular traces.

Soit M une algèbre de von Neumann et soit (Lp(M),p), 1p< l'espace Lp de Haagerup sur M. On montre que les propriétés de différentiabilité de p sont exactement les mêmes que celles obtenues sur les espaces Lp classiques (commutatifs). Les ingrédients principaux sont les opérateurs intégraux multiples et les traces singulières.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.017

Denis Potapov 1 ; Fedor Sukochev 1 ; Anna Tomskova 1 ; Dmitriy Zanin 1

1 School of Mathematics and Statistics, University of New South Wales, Kensington, NSW, 2052, Australia
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Denis Potapov; Fedor Sukochev; Anna Tomskova; Dmitriy Zanin. Fréchet differentiability of the norm of $ {L}_{p}$-spaces associated with arbitrary von Neumann algebras. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 923-927. doi : 10.1016/j.crma.2014.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.017/

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