Non-linear $\ast$-Jordan triple derivation on prime $\ast$-algebras

Vahid Darvish; Mojtaba Nouri; Mehran Razeghi; Ali Taghavi

Non-linear $\ast$-Jordan triple derivation on prime $\ast$-algebras

Operator Algebras 2019-11-12 v3

Authors: Vahid Darvish , Mojtaba Nouri , Mehran Razeghi , Ali Taghavi

Abstract

Let $\mathcal{A}$ be a prime $\ast$ -algebra and $\Phi$ preserves triple $\ast$ -Jordan derivation on $\mathcal{A}$ , that is, for every $A,B \in \mathcal{A}$ , $\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B\diamond C+A\diamond \Phi(B)\diamond C+A\diamond B\diamond \Phi(C)$ where $A\diamond B = AB + BA^{\ast}$ then $\Phi$ is additive. Moreover, if $\Phi(\alpha I)$ is self-adjoint for $\alpha\in\{1,i\}$ then $\Phi$ is a $\ast$ -derivation.

Keywords

prime *-algebra *-jordan triple derivation additive map self-adjoint *-derivation

Cite

@article{arxiv.1903.00451,
  title  = {Non-linear $\ast$-Jordan triple derivation on prime $\ast$-algebras},
  author = {Vahid Darvish and Mojtaba Nouri and Mehran Razeghi and Ali Taghavi},
  journal= {arXiv preprint arXiv:1903.00451},
  year   = {2019}
}

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12 pages

Non-linear $\ast$-Jordan triple derivation on prime $\ast$-algebras

Abstract

Keywords

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