Abstract
Let \(\mathcal{X}\) be a complex Banach space with \(\dim \mathcal{X}\geq 2\), and \(\mathcal{A} \subseteq \mathcal{B}(\mathcal{X})\) be a standard operator algebra. We show that a linear mapping \(\delta \colon \mathcal{A} \rightarrow \mathcal{A}\) is anti-derivable at zero (i.e., \(xy=0 \,{\rm in}\, \mathcal{A}\) implies \(y\delta(x)+\delta(y)x=0\)) if and only if \(\delta =0\).
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Fallahi, K., Ghahramani, H. Anti-derivable linear maps at zero on standard operator algebras. Acta Math. Hungar. 167, 287–294 (2022). https://doi.org/10.1007/s10474-022-01243-0
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DOI: https://doi.org/10.1007/s10474-022-01243-0