@article{Liang2026, 
author = {Xinfeng Liang and Ying Ning},
title = {Nonlinear    ξ-skew-Jordan triple higher derivations on prime    ∗-algebras},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {4},
pages = {2462-2480},
keywords = {nonlinear ξ-skew-Jordan triple higher derivation, additive higher ∗-derivation, unital ∗-algebras, standard operator algebras, von Neumann algebras},
url = {https://www.sciopen.com/article/10.3934/era.2026113},
doi = {10.3934/era.2026113},
abstract = {Let        B   denote a unital prime    ∗-algebra over the complex field        C  , and let    ξ  ∈      C    ∖  {  0  ,  ±  1  }. This paper characterized a family    Ψ  =  {      φ    m        }          m      ∈              N             of maps (not necessarily additive) from        B   into itself that satisfy the functional identity         φ    m    (  A      ⋄    ξ    B      ⋄    ξ    C  )  =      ∑          i      +      j      +      k      =      m            φ    i    (  A  )      ⋄    ξ        φ    j    (  B  )      ⋄    ξ        φ    k    (  C  )for all    A  ,  B  ,  C  ∈      B  , where    A      ⋄    ξ    B  =  A  B    +    ξ  B      A    ∗  . It was proved that    Ψ satisfies the above identity if and only if    Ψ is an additive higher    ∗-derivation and        φ    m    (  ξ  A  )  =  ξ      φ    m    (  A  ) holds for every    A  ∈      B  . As an application, the result not only generalizes the structure of nonlinear    ξ-skew-Jordan triple derivations on prime    ∗-algebras, but also yields a description of nonlinear    ξ-skew-Jordan triple higher derivations on several important operator algebras, including standard operator algebras and factor von Neumann algebras.}
}