Some Generalizations of ∗-Lie Derivable Mappings and Their Characterization on Standard Operator Algebras

We introduce generalizations of -Lie derivable mappings (which are not necessarily linear) on -algebras and then provide characterizations of these generalizations on standard operator algebras. Indeed, if H is an infinite dimensional complex Hilbert space and A be a unital standard operator algebra on H which is closed under the adjoint operation, then we characterize these mappings on A, especially we show that these mappings are linear. Our results are various generalizations of the main result of [W. Jing, Nonlinear ∗-Lie derivations of standard operator algebras, Quaestiones Math. 39 (2016), 1037–1046].