Non-linear ξ-Jordan *-derivations on von Neumann algebras

Abstract

AbstractLet be the algebra of all bounded linear operators on a complex Hilbert space and be a von Neumann algebra without central abelian projections. Let be a non-zero scalar. In this paper, it is proved that a mapping satisfies for all if and only if is an additive *-derivation and for all Keywords: *-derivationsξ-Jordan *-derivationsvon Neumann algebrasAMS Subject Classifications: 47B4946L10 AcknowledgmentsThe authors would like to thank the referee for their valuable comments and suggestions. The second author is supported by the National Natural Science Foundation of China (Grant No. 11171244). The third author is supported by the National Natural Science Foundation of China (Grant No. 11071188).