Mappings preserving product ab± ba^* on alternative W^*-factors

2020/12/20 by João Carlos da Motta Ferreira, Ferreira, João Carlos da Motta, Maria das Graças Bruno Marietto +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2012.11051

openalex publication_date 2020/12/20 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28

Abstract

Let A and B be two alternative W^*-factors. In this paper, we proved that a bijective mapping Φ:A→ B satisfies Φ(ab+ba^*)=Φ(a)Φ(b)+Φ(b)Φ(a)^* (resp., Φ(ab-ba^*)=Φ(a)Φ(b)-Φ(b)Φ(a)^*), for all elements a,b∈ A, if and only if Φ is a ∗ -ring isomorphism.

Citations

• When are multiplicative mappings additive?

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