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Nonlinear Mixed bi-Skew Jordan-Type and Skew Jordan Higher Derivations on ∗-Algebras
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Nonlinear Mixed bi-Skew Jordan-Type and Skew Jordan Higher Derivations on ∗-Algebras
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Journal Article
Nonlinear Mixed bi-Skew Jordan-Type and Skew Jordan Higher Derivations on ∗-Algebras
2026
Overview
Let A be a unital ∗-algebra over the complex field C, and let Ψ=ψmm∈N be a nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivation satisfies the relation ψm(L1⋄L2⋄…⋄Ln−1•Ln)=∑r1+…+rn=mψr1(L1)⋄…⋄ψrn−1(Ln−1)•ψrn(Ln), where L•N=LN+NL∗ and L⋄N=L∗N+N∗L for all L,N,Li∈A with i∈1,2,…,n. We demonstrate that every such higher derivation Ψ=ψmm∈N is an additive higher ∗-derivation. As an application, we use this result to characterize the structure of nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivations on a class of typical unital ∗-algebras, including standard operator algebras and von Neumann factors. This result also generalizes several existing results, in particular those concerning nonlinear mixed bi-skew Jordan-type and skew Jordan derivations on unital ∗-algebras.
Publisher
MDPI AG
