Nonlinear A*B+B*A Type Derivations on *-Algebras

Abstract

Let [see formula in PDF] be a unital *-algebra with the unit [see formula in PDF] and a nontrivial projection [see formula in PDF]. Suppose that [see formula in PDF] satisfies [see formula in PDF] implies [see formula in PDF] and [see formula in PDF] implies [see formula in PDF] In this paper, we prove that [see formula in PDF] is a nonlinear [see formula in PDF] type derivation on [see formula in PDF] if and only if [see formula in PDF] is an additive *-derivation. This is then applied to prime *-algebra, von Neumann algebras with no central summands of type [see formula in PDF] factor von Neumann algebras and standard operator algebras.