Linearity of (generalized) ?-Lie derivations and their structures on ?-algebras

Document Type

Article

Publication Date

4-1-2024

Abstract

Let A be a unital ?-algebra with characteristic not 2 and containing a nontrivial projection. We show that each nonlinear ?-Lie derivation on A is a linear ?-derivation. Moreover, we characterize nonlinear left ?-Lie centralizers and nonlinear generalized ?-Lie derivations. These results are applied to standard operator algebras and von Neumann algebras in complex Hilbert spaces, which generalize some known results.

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