Nonlinear $*$-Jordan-type derivations on alternative $*$-algebras
| Autor: | Andrade, Aline Jaqueline de Oliveira, Moraes, Gabriela C., Ferreira, Ruth Nascimento, Ferreira, Bruno Leonardo Macedo |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Siberian Electronic Mathematical Reports 19, 1 (2022), 125-137 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.33048/semi.2022.19.012 |
| Popis: | Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x = 0$ and $xA \cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $\Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $\Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras. Comment: 18 pages |
| Databáze: | arXiv |
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