Journal ArticleDOI
Nonlinear * -Lie derivations of standard operator algebras
TLDR
In this paper, it was shown that every nonlinear *-Lie derivation δ of 𝒜 is automatically linear and δ is an inner *-derivation.Abstract:
Let ℋ be an infinite dimensional complex Hilbert space and 𝒜 be a standard operator algebra on ℋ which is closed under the adjoint operation. We prove that every nonlinear *-Lie derivation δ of 𝒜 is automatically linear. Moreover, δ is an inner *-derivation.read more
Citations
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Nonlinear *-Lie-type derivations on standard operator algebras
TL;DR: In this article, it was shown that each nonlinear *-Lie-type derivation δ on an infinite dimensional complex Hilbert space is a linear *-derivation, and δ is an inner * -derivation as well.
Journal ArticleDOI
Multiplicative ∗-lie triple higher derivations of standard operator algebras
TL;DR: In this paper, it was shown that if A is closed under the adjoint operation, then every multiplicative ∗-Lie triple derivation d : A → B(H) is a linear inner higher derivation.
Journal ArticleDOI
Nonlinear $$\ast$$ * -Lie-type derivations on von Neumann algebras
TL;DR: In this paper, it was shown that a mapping from a complex Hilbert space to a von Neumann algebra without nonzero central abelian projections satisfies the additive *-derivation condition if and only if
Journal ArticleDOI
*-Jordan Semi-Triple Derivable Mappings
Lin Chen,Jianhua Zhang +1 more
TL;DR: In this article, the authors characterize the *-Jordan semi-triple derivable mappings (i.e., a mapping Φ from * algebra ��\mathcal{A}
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Nonlinear $\ast$-Jordan-Type Derivations on von Neumann Algebras
TL;DR: In this article, it was shown that a mapping of the von Neumann algebra of all bounded linear operators on a complex Hilbert space satisfies the condition that the mapping is an additive Jordan product.
References
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Journal ArticleDOI
Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings
TL;DR: In this article, the structures of commutativity-preserving mappings, Lie isomorphisms, and Lie derivations of certain prime rings are derived for all x ∈ R.
Journal ArticleDOI
When are multiplicative mappings additive
TL;DR: In this paper, the authors generalize the main theorem of Johnson's paper [l, p. 761, Theorem II] and at the same time remove the minimality condition.
Journal ArticleDOI
Nonlinear ∗-Lie derivations on factor von Neumann algebras
TL;DR: In this article, it was shown that every nonlinear ∗ -Lie derivation from a factor von Neumann algebra into itself is an additive ∗-derivation, which is the case for all nonlinear Lie derivations.