Geodesic
Nonlinear $*$-Jordan-type derivations on alternative $*$-algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 125-137

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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.
Keywords: $*$-Jordan-type derivation, $*$-derivation, alternative $*$-algebras. 
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     author = {A. J. O. Andrade and G. C. Moraes and R. N. Ferreira and B. L. M. Ferreira},
     title = {Nonlinear $*${-Jordan-type} derivations on alternative $*$-algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {125--137},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a5/}
}
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A. J. O. Andrade; G. C. Moraes; R. N. Ferreira; B. L. M. Ferreira. Nonlinear $*$-Jordan-type derivations on alternative $*$-algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 125-137. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a5/