Nonlinear Lie n-centralizers at zero-products on unital algebras

Key Points

• The research aims to explore the conditions under which a nonlinear map in unital algebras behaves predictably.
• Investigated maps that satisfy a specific polynomial condition in unital algebras.
• Applied findings to triangular algebras and certain von Neumann algebras.
• Analyzed the structure of the map to derive its form.
• Established that if a nonlinear map satisfies a given polynomial condition, it has a specific structure.
• Demonstrated that the difference between the map on a sum and the sum of maps lies in the center of the algebra.
• Identified that the nonlinear map can be expressed as a linear component plus an almost additive component.