March 3, 2026Open Access

Nonlinear mixed -Jordan type higher derivations on -algebras

Puntos clave

Nonlinear mixed *-Jordan-type higher derivations are shown to be additive higher *-derivations in unital *-algebras.
The study particularly focuses on classical unital *-algebras including prime *-algebras and von Neumann algebras of type I1.
Characterizations extend existing results, providing deeper insights into factor von Neumann algebras and operator algebras.
Significant implications arise for algebraic structures, potentially influencing future research in *-algebra theory.

Resumen

In this paper, we show that any nonlinear mixed *-Jordan-type higher derivation on unital *-algebras is an additive higher *-derivation. As applications, nonlinear mixed *-Jordan-type higher derivations on some classical unital *-algebras, such as prime *-algebras, von Neumann algebras of type I1, factor von Neumann algebras and standard operator algebras, are characterized, and some conclusions are extended.

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