Displaying similar documents to “Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products”

Generalized derivations associated with Hochschild 2-cocycles on some algebras

Jiankui Li, Jiren Zhou (2010)

Czechoslovak Mathematical Journal

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We investigate a new type of generalized derivations associated with Hochschild 2-cocycles which was introduced by A. Nakajima. We show that every generalized Jordan derivation of this type from CSL algebras or von Neumann algebras into themselves is a generalized derivation under some reasonable conditions. We also study generalized derivable mappings at zero point associated with Hochschild 2-cocycles on CSL algebras.

Characterization of Jordan derivations on 𝒥-subspace lattice algebras

Xiaofei Qi (2012)

Studia Mathematica

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Let 𝓛 be a 𝒥-subspace lattice on a Banach space X and Alg 𝓛 the associated 𝒥-subspace lattice algebra. Assume that δ: Alg 𝓛 → Alg 𝓛 is an additive map. It is shown that δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = 0 if and only if δ(A) = τ(A) + δ(I)A for all A, where τ is an additive derivation; if X is complex with dim X ≥ 3 and if δ is linear, then δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB...

On generalized Jordan derivations of Lie triple systems

Abbas Najati (2010)

Czechoslovak Mathematical Journal

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Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple θ -derivation on a Lie triple system is a θ -derivation.

Jordan *-derivation pairs on standard operator algebras and related results

Dilian Yang (2005)

Colloquium Mathematicae

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Motivated by Problem 2 in [2], Jordan *-derivation pairs and n-Jordan *-mappings are studied. From the results on these mappings, an affirmative answer to Problem 2 in [2] is given when E = F in (1) or when 𝓐 is unital. For the general case, we prove that every Jordan *-derivation pair is automatically real-linear. Furthermore, a characterization of a non-normal prime *-ring under some mild assumptions and a representation theorem for quasi-quadratic functionals are provided. ...

The Jordan structure of CSL algebras

Fangyan Lu (2009)

Studia Mathematica

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We show that every Jordan isomorphism between CSL algebras is the sum of an isomorphism and an anti-isomorphism. Also we show that each Jordan derivation of a CSL algebra is a derivation.

On Jordan mappings of inverse semirings

Sara Shafiq, Muhammad Aslam (2017)

Open Mathematics

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In this paper, the notions of Jordan homomorphism and Jordan derivation of inverse semirings are introduced. A few results of Herstein and Brešar on Jordan homomorphisms and Jordan derivations of rings are generalized in the setting of inverse semirings.

Derivations on Jordan-Banach algebras

A. Villena (1996)

Studia Mathematica

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We establish that all derivations on a semisimple Jordan-Banach algebra are automatically continuous. By showing that "almost all" primitive ideals in the algebra are invariant under a given derivation, the general case is reduced to that of primitive Jordan-Banach algebras.