Nonlinear mixed Jordan triple -derivations on factors

Let \(\mathcal{A}\) be a factor with dim\(\mathcal{A}\geq2\). For \(A, B\in\mathcal{A}\), define by \([A, B]_{*}=AB-BA^{\ast}\) and \(A\bullet B=AB+BA^{\ast}\) the new products of \(A\) and \(B\). In this paper, it is proved that a map \(\Phi: \mathcal {A}\rightarrow \mathcal {A}\) satisfies \(\Phi(...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Zhang, Dongfang, Li, Changjing
Format: Article
Language:English
Online Access:Get full text
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Summary:Let \(\mathcal{A}\) be a factor with dim\(\mathcal{A}\geq2\). For \(A, B\in\mathcal{A}\), define by \([A, B]_{*}=AB-BA^{\ast}\) and \(A\bullet B=AB+BA^{\ast}\) the new products of \(A\) and \(B\). In this paper, it is proved that a map \(\Phi: \mathcal {A}\rightarrow \mathcal {A}\) satisfies \(\Phi([A, B]_{*}\bullet C)=[\Phi(A), B]_{*}\bullet C+[A, \Phi(B)]_{*}\bullet C+[A, B]_{*}\bullet \Phi(C)\) for all \(A, B,C\in\mathcal {A}\) if and only if \(\Phi\) is an additive \(*-\)derivation.
ISSN:2331-8422