Results 241 to 250 of about 78,123 (278)

Characterizations of Jordan derivations and Jordan homomorphisms

Linear and Multilinear Algebra, 2011
Let 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
openaire   +1 more source

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
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +2 more sources

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 \(A,B\in \mathcal{A}\)).
openaire   +2 more sources

Derivation and Jordan operators

Integral Equations and Operator Theory, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seddik, A., Charles, J.
openaire   +1 more source

Ternary Derivations of Jordan Superalgebras

Algebra and Logic, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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 ...
openaire   +2 more sources

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.
openaire   +1 more source