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Characterizations of nonlinear Lie derivations of $B(X)$. (English) Zbl 1271.47029
Summary: Let $X$ be an infinite dimensional Banach space and $\Phi : B(X) \to B(X)$ be a nonlinear Lie derivation. Then $\Phi$ is the form $\delta + \tau$, where $\delta$ is an additive derivation of $B(X)$ and $\tau$ is a map from $B(X)$ into its center $Z_{B(X)}$, which maps commutators into the zero.

47B47Commutators, derivations, elementary operators, etc.
Full Text: DOI
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