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Additivity of Jordan Derivations on Jordan Algebras with Idempotents
Bulletin of the Iranian Mathematical Society, 2022Additivity is one of the most active topics in the study of mappings on rings and operator algebras. The aim of this paper is to study the additivity of Jordan derivations on Jordan algebras. The following result is obtained. Let \(J\) be a Jordan algebra with a nontrivial idempotent \(e\) and let \(J=J_1\oplus J_{\frac{1}{2}}\oplus J_0\) be the Peirce
Ferreira, Bruno L. M. +2 more
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Jordan, Jordan Right and Jordan Left Derivations on Convolution Algebras
Bulletin of the Iranian Mathematical Society, 2018A Jordan derivation on a ring $R$ is an additive mapping $d$ that satisfies \[ d(x^2) = d(x) x + x d(x) \] for all $x \in R$; $d$ is said to be a Jordan left derivation if \[ d(x^2) = 2xd(x) \] for all $x \in R$. Jordan right derivations are defined similarly.
Mohammad Hossein Ahmadi Gandomani
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Characterizations of Jordan derivations and Jordan homomorphisms
Linear and Multilinear Algebra, 2011Let 𝒜 be a unital Banach algebra and ℳ be a unital 𝒜-bimodule. We show that if δ is a linear mapping from 𝒜 into ℳ satisfying δ(ST) = δ(S)T +Sδ(T) for any S, T ∈ 𝒜 with ST = W, where W is a left or right separating point of ℳ, then δ is a Jordan derivation.
Jiankui Li, Jiren Zhou
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Derivations on Banach-Jordan Pairs
The Quarterly Journal of Mathematics, 2001A classical topic in the theory of Banach structures is the automatical continuity of derivations. From 1968, when Johnson and Sinclair proved the continuity of derivations acting on semisimple associative Banach algebras, until now, several algebraic conditions on a Banach algebra \(A\) which ensure the continuity of its derivations have been ...
Fernández López, A. +2 more
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JORDAN *-DERIVATIONS OF PRIME RINGS
Journal of Algebra and Its Applications, 2014Let R be a prime ring, which is not commutative, with involution * and with Qms(R) the maximal symmetric ring of quotients of R. An additive map δ : R → R is called a Jordan *-derivation if δ(x2) = δ(x)x* + xδ(x) for all x ∈ R. A Jordan *-derivation of R is called X-inner if it is of the form x ↦ xa - ax* for x ∈ R, where a ∈ Qms(R).
Lee, Tsiu-Kwen, Zhou, Yiqiang
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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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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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Jordan Higher Derivations of Incidence Algebras
Bulletin of the Malaysian Mathematical Sciences Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lizhen Chen, Zhankui Xiao
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Mathematical Journal of Okayama University, 1992
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 Stability of Jordan *-Derivation Pairs
Results in Mathematics, 2013Let \(A\) be a \(*\)-ring and \(X\) be an \(A\)-bimodule. If \(L, R:A \to X\) are additive mappings such that \(L(a^3)=L(a)\cdot (a^*)^2+a\cdot R(a)\cdot a^*+a^2L(a)\) and \(R(a^3)=R(a) \cdot(a^*)^2+a\cdot L(a)\cdot a^*+a^2R(a)\) for all \(a\in A\), then \((L,R)\) is called a Jordan \(*\)-derivation pair. In this paper, the authors prove the Hyers-Ulam
Bodaghi, Abasalt +2 more
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