Geodesic
Nonlinear bi-skew Jordan-type derivations on factor von Neumann algebras
Filomat, Tome 37 (2023) no. 17, p. 5591

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DOI

Let T be a factor von Neumann algebra acting on complex Hilbert space with dim(T) ≥ 2. For any T,T1,T2, . . . ,Tn ∈ T, define q1(T) = T, q2(T1,T2) = T1 ⋄ T2 = T1T∗2 + T2T∗1 and qn(T1, . . . ,Tn) = qn−1(T1, . . . ,Tn−1) ⋄ Tn for all integers n ≥ 2. In this article, we prove that a map ζ : T → T satisfies ζ(qn(T1, . . . ,Tn)) = ∑n i=1 qn(T1, . . . ,Ti−1, ζ(Ti),Ti+1, . . . ,Tn) for all T1, . . . ,Tn ∈ T if and only if ζ is an additive ∗-derivation.
DOI : 10.2298/FIL2317591A
Classification : 16W25, 46L10
Keywords: Additive ∗-derivation, Bi-skew Jordan-type derivation, Factor von Neumann algebra 
Mohammad Ashraf; Shamim Akhter; Mohammad Afajal Ansari. Nonlinear bi-skew Jordan-type derivations on factor von Neumann algebras. Filomat, Tome 37 (2023) no. 17, p. 5591 . doi: 10.2298/FIL2317591A
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     title = {Nonlinear bi-skew {Jordan-type} derivations on factor von {Neumann} algebras},
     journal = {Filomat},
     pages = {5591 },
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     doi = {10.2298/FIL2317591A},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2317591A/}
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