Nonlinear ξ-Jordan triple *-derivation on prime *-algebras

Fangjuan Zhang

doi:10.1216/rmj.2022.52.323

Abstract

Let ${\mathcal{A}}$ be a prime $*$ -algebra and let $\xi \in {\mathbb(C)} \setminus \{ 0, \pm 1\}$ . We prove that a mapping $\phi : {\mathcal{A}} \to {\mathcal{A}}$ satisfies

$\phi (A{{\Diamond}_\xi }B{{\Diamond}_\xi }C) = \phi (A){{\Diamond}_\xi }B{{\Diamond}_\xi }C + A{{\Diamond}_\xi }\phi (B){{\Diamond}_\xi }C + A{{\Diamond}_\xi }B{{\Diamond}_\xi }\phi (C)$

for all $A,B,C \in {\mathcal{A}}$ if and only if $\phi$ is an additive $*$ -derivation and $\phi (\xi A) = \xi \phi (A)$ for all $A \in {\mathcal(A)}$ .

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Fangjuan Zhang. "Nonlinear $\xi$ -Jordan triple $*$ -derivation on prime $*$ -algebras." Rocky Mountain J. Math. 52 (1) 323 - 333, February 2022. https://doi.org/10.1216/rmj.2022.52.323

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Received: 25 October 2020; Revised: 21 May 2021; Accepted: 26 May 2021; Published: February 2022

First available in Project Euclid: 19 April 2022

MathSciNet: MR4409933

zbMATH: 07524627

Digital Object Identifier: 10.1216/rmj.2022.52.323

Subjects:

Primary: 46J10 , 46L10 , 47B48

Keywords: additive map , Jordan triple derivation , prime *-algebra

Abstract

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