Comptes Rendus
Operator theory
Derivations with values in noncommutative symmetric spaces
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1357-1365.

Let E=E(0,) be a symmetric function space and E(,τ) be the noncommutative symmetric space corresponding to E(0,) 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:𝒜E(,τ) is necessarily inner for each C * -subalgebra 𝒜 in the class of all semifinite von Neumann algebras as those with the Levi property.

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DOI: 10.5802/crmath.508
Keywords: derivation, noncommutative symmetric space, semifinite von Neumann algebra

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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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