Characterizations of Jordan mappings on some rings and algebras through zero products

2016/11/14 by Huang, Wenbo, Li, Jiankui, He, Jun
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1611.04274

Abstract

Let U=[ A · amp; M N · amp; B ] be a generalized matrix ring, where A and B are 2-torsion free. We prove that if ϕ:U→ U is an additive mapping such that ϕ(U)∘ V+U∘ ϕ(V)=0 whenever UV=VU=0, then ϕ=δ+η, where δ is a Jordan derivation and η is a multiplier. As its applications, we prove that the similar conclusion remains valid on full matrix algebras, unital prime rings with a nontrivial idempotent, unital standard operator algebras, CDCSL algebras and von Neumann algebras.

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