Nonlinear Mixed Bi-Skew Jordan-Type Higher Derivations on *-Algebras

Key Points

• The aim is to explore the nature of nonlinear mixed bi-skew Jordan-type higher derivations in unital *-algebras.
• Defined a unital *-algebra with a nontrivial projection.
• Analyzed the characteristics of mixed bi-skew Jordan-type higher derivations.
• Demonstrated the additivity property in higher *-derivations.
• Confirmed that every nonlinear mixed bi-skew Jordan-type higher derivation is an additive higher *-derivation.
• Applied findings to prime *-algebras, factor von Neumann algebras, and standard operator algebras.