On the Characterization of Non-linear Mixed Bi-skew Jordan Triple Derivations on ∗-Algebras.
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Authors: M. ASHRAF, MD A. MADNI, MD S. AKHTER AND M. R. MOZUMDER
DOI: 10.46793/KgJMat2608.1207A
Abstract:
In this article, it is shown that a map ξ : ???? → ???? (not necessarily linear) satisfies ξ((A ∘ B) ∙ C) = (ξ(A) ∘ B) ∙ C + (A ∘ ξ(B)) ∙ C + (A ∘ B) ∙ ξ(C) holds for all A,B,C ∈ ???? if and only if ξ is an additive ∗-derivation where ???? a unital ∗-algebra over the complex fields ℂ. As applications, we apply our main result to some special classes of unital ∗-algebras such as prime ∗-algebras, standard operator algebras, factor von Neumann algebras and von Neumann algebras with no central summands of type I1.
Keywords:
Additive ∗-derivation, mixed bi-skew Jordan triple derivation, ∗-algebras, Von Neumann algebra.
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