$*$-Lie Derivable Mappings on Von Neumann Algebras

Abstract

In this paper, we prove that every $*$-Lie derivable mapping on a von Neumann algebra with no central abelian projections can be expressed as the sum of an additive $*$-derivation and a mapping with image in the center vanishing at commutators.

Keywords

$*$-Lie derivable mapping')">$*$-Lie derivable mapping / Derivation / Von Neumann algebra

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Funding

Natural Science Foundation of Shandong Province, China(ZR2015PA010)

National Natural Science Foundation of China(11401273)