$$*$$ ∗ -Lie Derivable Mappings on Von Neumann Algebras

Li, Changjing; Chen, Quanyuan; Wang, Ting

doi:10.1007/s40304-015-0077-7

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…Yu and Zhang [22] proved that every * -Lie derivable mapping from a factor von Neumann algebra into itself is an additive * -derivation. Also, Li, Chen and Wang [14] obtained the same result for * -Lie derivable mappings on a von Neumann algebras and proved that every * -Lie derivable mapping on a von Neumann algebra with no central abelian projections can be expressed as the sum of an additive * -derivation and a mapping with image in the centre vanishing at commutators. In addition, the characterization of Lie derivations and * -Lie derivations on various algebras are considered in [2], [4], [5], [8], [7], [9], [13], [15], [20], [23].…”

Section: Introductionmentioning

confidence: 69%

∗-Lie higher derivable mappings on ∗-rings

Ashraf¹,

Akhtar²,

Wani³

2020

APAM

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Let R be a * -ring with the center Z(R) and N be the set of all non-negative integers. Let L = {L n } n∈N be the family of mappings L n : R → R (not necessarily additive) such that L 0 = I R , the identity mapping of R. Then L is said to be a * -Lie higher derivable mapping of] holds for all X, Y ∈ R. In this paper, it is shown that, if R is a * -ring containing a nontrivial self adjoint idempotent which admits a * -Lie higher derivable mapping L = {L n } n∈N , then there exists an element Z X,Y (depending on X and Y ) in the center Z(R) such that L n (X + Y ) = L n (X) + L n (Y ) + Z X,Y .

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Section: Introductionmentioning

confidence: 69%

∗-Lie higher derivable mappings on ∗-rings

Ashraf¹,

Akhtar²,

Wani³

2020

APAM

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“…Yu and Zhang [19] proved that every * -Lie derivable mapping from a factor von Neumann algebra into itself is an additive * -derivation. Also, Li, Chen and Wang [9] obtained the same result for * -Lie derivable mappings on von Neumann algebras and proved that every * -Lie derivable mapping on a von Neumann algebra with no central abelian projections can be expressed as the sum of an additive * -derivation and a mapping with image in the centre vanishing on commutators. In addition, the characterization of Lie derivations and * -Lie derivations on various algebras are considered in [1], [2], [5], [4], [6], [8], [12], [13], [17], [20].…”

Section: Introductionmentioning

confidence: 70%

“…Motivated by the results due to W. Jing & F. Lu [8] and C. Li et al [9], in Section 2, we investigate the additivity of * -Lie derivable mappings on * -rings and show that every * -Lie derivable mapping on R is almost additive in the sense that for any U,…”

Section: Introductionmentioning

confidence: 99%

Characterizations of ∗-Lie derivable mappings on prime ∗-rings

Al-Kenani¹,

Ashraf²,

Wani³

2019

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znano

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Let R be a *-ring containing a nontrivial self-adjoint idempotent. In this paper it is shown that under some mild conditions on R, if a mapping d : R → R satisfies d([U * , V ]) = [d(U) * , V ] + [U * , d(V)] for all U, V ∈ R, then there exists Z U,V ∈ Z(R) (depending on U and V), where Z(R) is the center of R, such that d(U + V) = d(U) + d(V) + Z U,V. Moreover, if R is a 2-torsion free prime *-ring additionally, then d = ψ + ξ, where ψ is an additive *-derivation of R into its central closure T and ξ is a mapping from R into its extended centroid C such that ξ(U + V) = ξ(U) + ξ(V) + Z U,V and ξ([U, V ]) = 0 for all U, V ∈ R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras.

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