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arXiv · 2105.00955

Nonlinear $*$-Jordan-type derivations on alternative $*$-algebras

Aline Jaqueline de Oliveira Andrade·Gabriela C. Moraes·Ruth Nascimento Ferreira·Bruno Leonardo Macedo Ferreira
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Abstract

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.

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Aline Jaqueline de Oliveira Andrade, Gabriela C. Moraes, Ruth Nascimento Ferreira, Bruno Leonardo Macedo Ferreira. 2021-04-23. Nonlinear $*$-Jordan-type derivations on alternative $*$-algebras. https://doi.org/10.33048/semi.2022.19.012

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