Soit une algèbre de von Neumann et soit , l'espace de Haagerup sur . On montre que les propriétés de différentiabilité de sont exactement les mêmes que celles obtenues sur les espaces classiques (commutatifs). Les ingrédients principaux sont les opérateurs intégraux multiples et les traces singulières.
Let be a von Neumann algebra and let , be Haagerup's -space on . We prove that the differentiability properties of are precisely the same as those of classical (commutative) -spaces. Our main instruments are multiple operator integrals and singular traces.
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Denis Potapov 1 ; Fedor Sukochev 1 ; Anna Tomskova 1 ; Dmitriy Zanin 1
@article{CRMATH_2014__352_11_923_0, author = {Denis Potapov and Fedor Sukochev and Anna Tomskova and Dmitriy Zanin}, title = {Fr\'echet differentiability of the norm of $ {L}_{p}$-spaces associated with arbitrary von {Neumann} algebras}, journal = {Comptes Rendus. Math\'ematique}, pages = {923--927}, publisher = {Elsevier}, volume = {352}, number = {11}, year = {2014}, doi = {10.1016/j.crma.2014.09.017}, language = {en}, }
TY - JOUR AU - Denis Potapov AU - Fedor Sukochev AU - Anna Tomskova AU - Dmitriy Zanin TI - Fréchet differentiability of the norm of $ {L}_{p}$-spaces associated with arbitrary von Neumann algebras JO - Comptes Rendus. Mathématique PY - 2014 SP - 923 EP - 927 VL - 352 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2014.09.017 LA - en ID - CRMATH_2014__352_11_923_0 ER -
%0 Journal Article %A Denis Potapov %A Fedor Sukochev %A Anna Tomskova %A Dmitriy Zanin %T Fréchet differentiability of the norm of $ {L}_{p}$-spaces associated with arbitrary von Neumann algebras %J Comptes Rendus. Mathématique %D 2014 %P 923-927 %V 352 %N 11 %I Elsevier %R 10.1016/j.crma.2014.09.017 %G en %F CRMATH_2014__352_11_923_0
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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