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Jordan $\ast$-derivations with respect to the Jordan product
Publicationes Mathematicae Debrecen, 1996Summary: In this note, we give a description of Jordan \(*\)-derivations on standard operator algebras with respect to the Jordan product defined by \(A\circ B =\frac 12 (AB +BA)\). That is, we characterize the additive solutions of the functional equation \(E(T \circ T) = T \circ E(T) + E(T) \circ T^*\) (\(T \in A\)), where \(\mathcal A\subset ...
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Generalized Jordan Derivations
2001We define a notion of generalized Jordan (resp. Lie) derivations and give some elementary properties of generalized Jordan (resp. Lie) derivations. These categorical results correspond to the results of generalized derivations in [N]. Moreover, we extend Herstein’s result of Jordan derivations on a prime ring to generalized Jordan derivations.
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Jordan higher derivations, a new approach
2022Summary: Let \(\mathcal{A}\) be a unital algebra over a 2-torsion free commutative ring \(\mathcal{R}\) and \(\mathcal{M}\) be a unital \(\mathcal{A}\)-bimodule. We show that every Jordan higher derivation \(D=\{D_n\}_{n\in \mathbb{N}_0}\) from the trivial extension \(\mathcal{A} \ltimes \mathcal{M}\) into itself is a higher derivation, if \(PD_1(QXP)Q=
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Notes on Jordan (σ, τ)*-derivations and Jordan triple (σ, τ)*-derivations
Aequationes mathematicae, 2012Let R be a 2-torsion free semiprime *-ring, σ, τ two epimorphisms of R and f, d : R → R two additive mappings. In this paper we prove the following results: (i) d is a Jordan (σ, τ)*-derivation if and only if d is a Jordan triple (σ, τ)*-derivation. (ii) f is a generalized Jordan (σ, τ)*-derivation if and only if f is a generalized Jordan triple (σ, τ)*
Öznur Gölbaşı, Emine Koç
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JORDAN *-DERIVATIONS AND QUADRATIC JORDAN *-DERIVATIONS ON REAL C*-ALGEBRAS AND REAL JC*-ALGEBRAS
International Journal of Geometric Methods in Modern Physics, 2013In this work, we introduce quadratic Jordan *-derivations on real C*-algebras and real JC*-algebras and prove the Hyers–Ulam stability of Jordan *-derivations and of quadratic Jordan *-derivations on real C*-algebras and real JC*-algebras. We also establish the superstability of such derivations on real C*-algebras and real JC*-algebras by using a ...
Bodaghi, Abasalt, Park, Choonkil
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2016
Let \(R\) be a ring and \(X\) be a left \(R\)-module such that \(aRx = 0\), where \(a \in R\) and \(x \in X\), implies \(a = 0\) or \(x = 0\). Suppose there exists a nonzero additive map \(D : R \to X\) satisfying \(D(a^ 2) = 2aD(a)\) for every \(a \in R\) (such maps are called Jordan left derivations). \textit{J. Vukman} and the reviewer [Proc.
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Let \(R\) be a ring and \(X\) be a left \(R\)-module such that \(aRx = 0\), where \(a \in R\) and \(x \in X\), implies \(a = 0\) or \(x = 0\). Suppose there exists a nonzero additive map \(D : R \to X\) satisfying \(D(a^ 2) = 2aD(a)\) for every \(a \in R\) (such maps are called Jordan left derivations). \textit{J. Vukman} and the reviewer [Proc.
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On the norm of Jordan \(*\)-derivations
2020In this paper, the authors are interested in the norm of the inner Jordan *-derivation acting on the Banach algebra of all bounded linear operators. Using the maximal numerical range, the authors give some lower bounds.
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Notes on Jordan \((\sigma,\tau)^*\)-derivations and Jordan triple \((\sigma,\tau)^*\)-derivations.
2013WOS ...
Golbasi, Oznur, Koc, Emine
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Jordan derivable mappings on $$B(H)$$
Acta Mathematica HungaricaLet \(H\) be a Hilbert space. In this paper, sufficient conditions are given for the existence of Jordan derivations and Jordan generalized derivations over \(B(H)\). The following is the main result. \par Theorem. Let \(H\) be a real or complex Hilbert space with \(\operatorname{dim}(H)\ge 2\) and \(\Omega\in B(H)\) be given.
Chen, L., Guo, F., Qin, Z.-J.
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Generalized Lie (Jordan) Triple Derivations on Arbitrary Triangular Algebras
Bulletin of the Malaysian Mathematical Sciences Society, 2021Mohammad Ashraf +2 more
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