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

Abstract

Let be a generalized matrix ring, where and are 2-torsion free. We prove that if is an additive mapping such that whenever then , where is a Jordan derivation and 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.

Keywords:

• Derivation
• generalized matrix ring
• Jordan derivation
• multiplier
• von Neumann algebra

AMS Subject Classifications:

• 16W25
• 46L57
• 47B47

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper was partially supported by National Natural Science Foundation of China [grant number 11371136].