Derivations with values in noncommutative symmetric spaces

Jinghao Huang; Fedor Sukochev

doi:10.5802/crmath.508

Théorie des opérateurs

Derivations with values in noncommutative symmetric spaces

Jinghao Huang ¹ ; Fedor Sukochev ²

¹ Institute for Advanced Study in Mathematics of HIT, Harbin Institute of Technology, Harbin, 150001, China
² School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, Australia

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1357-1365.

Résumé

Let $E = E (0, \infty)$ be a symmetric function space and $E (ℳ, τ)$ be the noncommutative symmetric space corresponding to $E (0, \infty)$ associated with a von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of spaces $E$ for which every derivation $δ : 𝒜 \to E (ℳ, τ)$ is necessarily inner for each $C^{*}$ -subalgebra $𝒜$ in the class of all semifinite von Neumann algebras $ℳ$ as those with the Levi property.

Reçu le : 2023-01-28
Accepté le : 2023-04-21
Publié le : 2023-10-31

DOI : 10.5802/crmath.508

Mots clés : derivation, noncommutative symmetric space, semifinite von Neumann algebra

Affiliations des auteurs :

Jinghao Huang ¹ ; Fedor Sukochev ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Derivations with values in noncommutative symmetric spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1357--1365},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2023},
     doi = {10.5802/crmath.508},
     language = {en},
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Jinghao Huang; Fedor Sukochev. Derivations with values in noncommutative symmetric spaces. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1357-1365. doi : 10.5802/crmath.508. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.508/

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