Nonlinear mixed Jordan triple *-derivations on factors

2021/12/08 by Dongfang Zhang, Changjing Li, Zhang, Dongfang +1
Computer Science · Mathematics · #46L10 #47B47 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Nonlinear Differential Equations Analysis #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2112.04486

openalex publication_date 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a factor with dimA≥2. For A, B\inA, define by [A, B]_*=AB-BA^∗ and A\bullet B=AB+BA^∗ the new products of A and B. In this paper, it is proved that a map Φ: \mathcal A→ \mathcal A satisfies Φ([A, B]_*\bullet C)=[Φ(A), B]_*\bullet C+[A, Φ(B)]_*\bullet C+[A, B]_*\bullet Φ(C) for all A, B,C∈\mathcal A if and only if Φ is an additive *-derivation.

Related

• Nonlinear mixed Jordan triple *-derivations on *-algebras
• Non-linear ∗-Jordan derivations on von Neumann algebras
• Nonlinear maps preserving the mixed Jordan triple η-*-product between factors
• Non-linear ∗-Jordan triple derivation on prime ∗-algebras
• Non-Linear New Product A^*B-B^*A Derivations on ∗-Algebras