Nonlinear skew lie triple derivations between factors

“…Note that, unlike von Neumann algebras which are always weakly closed, a standard operator algebra is not necessarily closed. The current work together with [7,[10][11][12][13][23][24][25][26] indicates that it is feasible to investigate * -Jordan-type derivations and * -Lie-type derivations on operator algebras under a unified framework-η- * -Jordan-type derivations. We have good reasons to believe that characterizing η- * -Jordan-type derivations on operator algebras is also of great interest.…”

Section: Related Topics For Future Researchmentioning

confidence: 99%

“…η- * -Jordan 2-derivations, η- * -Jordan 3-derivations and η- * -Jordan n-derivations are collectively referred to as η- * -Jordan-type derivations. η- * -Jordan-type derivations on operator algebras are intensively studied by several authors,[7,[10][11][12][13][23][24][25][26] . A basic question in this line is to investigate whether each nonlinear η- * -Jordan-type derivation on an operator algebra A with * is an additive * -derivation.…”

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confidence: 99%

Nonlinear $\ast$-Jordan-Type Derivations on von Neumann Algebras

Lin

2018

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Let H be a complex Hilbert space, B(H) be the algebra of all bounded linear operators on H and A ⊆ B(H) be a von Neumann algebra without central summands of type I 1 . For arbitrary elements A, B ∈ A, one can define their * -Jordan product in the sense of A ⋄ B = AB + BA * . Let pn(x 1 , x 2 , • • • , xn) be the polynomial defined by n indeterminates x 1 , • • • , xn and their * -Jordan products. In this article, it is shown that a mapping δ : A −→ B(H) satisfies the conditionand only if δ is an additive * -derivation.

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“…, on every factor von Neumann algebra A ⊆ B(H) is an additive * −derivation. the authors in [9] introduced the concept of Skew Lie triple derivations. A map…”

Section: Introductionmentioning

confidence: 99%

Non-linear λ−jordan Triple∗−derivation on Prime ∗−algebras

Kaheshzad,

Rahnaward,

Rahimi

2024

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Let $\mathcal{A}$ be a prime $\ast-$algebra and $\Phi$ a $\lambda-$Jurdan triple derivation on A, that is, for every $A, B, C \in \mathcal{A}$, $\Phi(A\diamond B)=\Phi(A)\diamond B+ A\diamond\Phi(B)$ wher $A\diamond_\lambda B = AB^\ast +\lambda BA$ such that a real scalar $|\lambda|\ne 0, 1,$ and $\Phi$ is additive. moreover, if $\Phi(I)$ and $\Phi(il)$ are selfadjiont then $\Phi$ is a $\ast-$derivation.

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Nonlinear skew lie triple derivations between factors

Cited by 57 publications

References 14 publications

Nonlinear mixed Jordan triple ∗-derivations on factor von Neumann algebras

Nonlinear mixed Jordan triple ∗-derivations on factor von Neumann algebras

Nonlinear $\ast$-Jordan-Type Derivations on von Neumann Algebras

Non-linear λ−jordan Triple∗−derivation on Prime ∗−algebras

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