Results 271 to 280 of about 1,329 (298)

Jordan Derivations of Reflexive Algebras

Integral Equations and Operator Theory, 2010
Let \(\mathcal{A}\) be an algebra and \(\mathcal{M}\) be an \(\mathcal{A}\)-bimodule. A linear map \(\delta : \mathcal{A}\rightarrow \mathcal{M}\) is called a Jordan derivation (resp., a derivation) if \(\delta(A^2) = \delta(A)A + A\delta(A)\) for all \(A\in \mathcal{A}\) (resp., \(\delta(AB) = \delta(A)B + A\delta(B)\) for all \(A,B\in \mathcal{A}\)).
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Jordan derivation of certain Jordan matrix algebras

Linear and Multilinear Algebra, 2008
Let R be an arbitrary 2-torsionfree commutative ring, M(n, R) the matrix algebra consisting of all n × n matrices over R, S(n, R) (resp., D(n, R)) the subset of M(n, R) consisting of all symmetric (resp., diagonal) ones. In this article, we first determine all the Jordan subalgebras of S(n, R) containing D(n, R), then for any given Jordan subalgebra of
Dengyin Wang, Qian Hu, Chunguang Xia
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Ternary Derivations of Jordan Superalgebras

Algebra and Logic, 2014
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Derivation and Jordan operators

Integral Equations and Operator Theory, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seddik, A., Charles, J.
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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, 2013
In 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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Random Jordan Derivations

1994
A classical nonassociative operators topic is the continuity of Jordan derivations on Banach algebras which have some aditional property. We recall that a Jordan derivation on a Banach algebra A is a linear mapping D : A → A such that D(a 2) = D(a)a + aD(a), ∀a ∈ A, or equivalently satisfying that D(a • b) = D (a) • b + a • D(b), ∀a, b ∈ A, (where, as ...
Maria Victoria Velasco, Armando R. Villena   +1 more
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Characterization of Jordan homomorphisms and Jordan derivations

Summary: We show that if \(f:A\to B\) is a continuous linear map between Banach algebras satisfying \(f(a\circ b)=f(a)\circ f(b)\) for all \(a,b\in A\) with \(a\circ b=e_A\) or \(ab=ba=e_A\), then \(f\) is a Jordan homomorphism. It is also proved that if \(\delta:A\to X\) is a continuous linear map satisfying \(\delta(a\circ b)=\delta(a)b+a\delta(b ...
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Jordan higher derivations, a new approach

2022
Summary: 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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Jordan decomposable derivations

Communications in Algebra, 1988
A derivation is called Jordan decomposable i-f it can be decomposed into a sum of commuting nil and semi-simple parts. In this paper, we study a subfamily of such derivations, the strongly decomposable derivations. After establishing some basic properties, we present an intrinsic criterion for such a derivation.
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Notes on Jordan \((\sigma,\tau)^*\)-derivations and Jordan triple \((\sigma,\tau)^*\)-derivations.

2013
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Golbasi, Oznur, Koc, Emine
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