Results 231 to 240 of about 865 (267)

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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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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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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Weak Jordan *-derivations of prime rings

Journal of Algebra and Its Applications, 2022
Let * be an involution of a non-commutative prime ring [Formula: see text] with the maximal symmetric ring of quotients and the extended centroid of [Formula: see text] denoted by [Formula: see text] and [Formula: see text], respectively. Consider [Formula: see text] be an additive map, if [Formula: see text] for all [Formula: see text], then such a ...
Siddeeque, Mohammad Aslam, Khan, Nazim, Abdullah, Ali Ahmed   +2 more
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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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Derivation and Jordan operators

Integral Equations and Operator Theory, 1997
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Seddik, A., Charles, J.
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Ternary Derivations of Jordan Superalgebras

Algebra and Logic, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Jordan $\ast$-derivations with respect to the Jordan product

Publicationes Mathematicae Debrecen, 1996
Summary: 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

2001
We 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

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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