English

Nonlinear mixed Jordan triple *-derivations on factors

Operator Algebras 2022-03-23 v2

Abstract

Let A\mathcal{A} be a factor with dimA2\mathcal{A}\geq2. For A,BAA, B\in\mathcal{A}, define by [A,B]=ABBA[A, B]_{*}=AB-BA^{\ast} and AB=AB+BAA\bullet B=AB+BA^{\ast} the new products of AA and BB. In this paper, it is proved that a map Φ:AA\Phi: \mathcal {A}\rightarrow \mathcal {A} satisfies Φ([A,B]C)=[Φ(A),B]C+[A,Φ(B)]C+[A,B]Φ(C)\Phi([A, B]_{*}\bullet C)=[\Phi(A), B]_{*}\bullet C+[A, \Phi(B)]_{*}\bullet C+[A, B]_{*}\bullet \Phi(C) for all A,B,CAA, B,C\in\mathcal {A} if and only if Φ\Phi is an additive *-derivation.

Keywords

Cite

@article{arxiv.2112.04486,
  title  = {Nonlinear mixed Jordan triple *-derivations on factors},
  author = {Dongfang Zhang and Changjing Li},
  journal= {arXiv preprint arXiv:2112.04486},
  year   = {2022}
}

Comments

There was an error in Claim 7 of Theorem 2.4

R2 v1 2026-06-24T08:09:34.964Z