Derivations with values in noncommutative symmetric spaces

Huang, Jinghao; Sukochev, Fedor

Comptes Rendus. Mathématique, Tome 361 (2023) no. G8, pp. 1357-1365

Let $E=E(0,\infty )$ be a symmetric function space and $E(ℳ,\tau )$ 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 $\delta :𝒜\to E(ℳ,\tau )$ is necessarily inner for each $C^{*}$-subalgebra $𝒜$ in the class of all semifinite von Neumann algebras $ℳ$ as those with the Levi property.

Keywords: derivation, noncommutative symmetric space, semifinite von Neumann algebra

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