scholarly journals On generalized Jordan ∗-derivation in rings

2014 ◽  
Vol 22 (1) ◽  
pp. 11-13 ◽  
Author(s):  
Nadeem ur Rehman ◽  
Abu Zaid Ansari ◽  
Tarannum Bano
Keyword(s):  
Jordan Derivation ◽  
Generalized Jordan Derivation

scholarly journals Generalized Jordan derivation on nest algebras

2009 ◽  
Vol 430 (5-6) ◽  
pp. 1479-1485 ◽  
Author(s):  
Jinchuan Hou ◽  
Xiaofei Qi
Keyword(s):  
Jordan Derivation ◽  
Nest Algebras ◽  
Generalized Jordan Derivation

scholarly journals New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal

2021 ◽  
Vol 54 (1) ◽  
pp. 311-317
Author(s):  
Hadia Messaoudene ◽  
Nadia Mesbah
Keyword(s):  
Identity Operator ◽  
Jordan Derivation ◽  
Basic Properties ◽  
New Class ◽  
Generalized Jordan Derivation

Abstract A new class of operators, larger than ∗ \ast -finite operators, named generalized ∗ \ast -finite operators and noted by Gℱ ∗ ( ℋ ) {{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }}) is introduced, where: Gℱ ∗ ( ℋ ) = { ( A , B ) ∈ ℬ ( ℋ ) × ℬ ( ℋ ) : ∥ T A − B T ∗ − λ I ∥ ≥ ∣ λ ∣ , ∀ λ ∈ C , ∀ T ∈ ℬ ( ℋ ) } . {{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }})=\{(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}):\parallel TA-B{T}^{\ast }-\lambda I\parallel \ge | \lambda | ,\hspace{0.33em}\forall \lambda \in {\mathbb{C}},\hspace{0.33em}\forall T\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\}. Basic properties are given. Some examples are also presented.

scholarly journals Nearly generalized Jordan derivations

2011 ◽  
Vol 61 (1) ◽  
Author(s):  
M. Eshaghi Gordji ◽  
N. Ghobadipour
Keyword(s):  
Linear Mapping ◽  
Usual Sense ◽  
Jordan Derivation ◽  
Generalized Jordan Derivation ◽  
Rassias Stability

AbstractLet A be an algebra and let X be an A-bimodule. A ∂-linear mapping d: A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ: A → X such that d(a 2) = ad(a)+δ(a)a for all a ∈ A. The main purpose of this paper is to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

scholarly journals Generalized Jordan Derivations of Incidence Algebras

2019 ◽  
pp. 483-490
Author(s):  
Ruth Nascimento Ferreira ◽  
Bruno Leonardo Macedo Ferreira
Keyword(s):  
Ordered Set ◽  
Generalized Derivation ◽  
Jordan Derivation ◽  
Locally Finite ◽  
Incidence Algebra ◽  
Incidence Algebras ◽  
Generalized Jordan Derivation ◽  
Torsion Free

For a given ring $\Re$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \Re)$ to be the incidence algebra of $X$ over $\Re$. Motivated by a Xiao’s result which states that every Jordan derivation of $I(X, \Re)$ is a derivation in the case $\Re$ is 2-torsion free, one proves that each generalized Jordan derivation of $I(X, \Re)$ is a generalized derivation provided $\Re$ is 2-torsion free, getting as a consequence the above mentioned result.

scholarly journals GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS

2019 ◽  
Vol 109 (1) ◽  
pp. 36-43
Author(s):  
BRUNO L. M. FERREIRA ◽  
RUTH N. FERREIRA ◽  
HENRIQUE GUZZO
Keyword(s):  
Generalized Derivation ◽  
Idempotent Element ◽  
Jordan Derivation ◽  
Mild Conditions ◽  
Generalized Jordan Derivation ◽  
Semiprime Rings

The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.

A NOTE ON -JORDAN DERIVATIONS OF RINGS AND BANACH ALGEBRAS

2015 ◽  
Vol 93 (2) ◽  
pp. 231-237 ◽  
Author(s):  
IRENA KOSI-ULBL ◽  
JOSO VUKMAN
Keyword(s):  
Semiprime Ring ◽  
Banach Algebras ◽  
Additive Mapping ◽  
Jordan Derivation ◽  
Torsion Free

In this paper we prove the following result: let$m,n\geq 1$be distinct integers, let$R$be an$mn(m+n)|m-n|$-torsion free semiprime ring and let$D:R\rightarrow R$be an$(m,n)$-Jordan derivation, that is an additive mapping satisfying the relation$(m+n)D(x^{2})=2mD(x)x+2nxD(x)$for$x\in R$. Then$D$is a derivation which maps$R$into its centre.

scholarly journals Derivations on Lie Ideals of σ-Prime Γ-Rings

2015 ◽  
Vol 39 (2) ◽  
pp. 249-255
Author(s):  
Md Mizanor Rahman ◽  
Akhil Chandra Paul
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Jordan Derivation ◽  
Lie Ideal ◽  
Square Closed Lie Ideal ◽  
Academy Of Sciences ◽  
Gamma Rings ◽  
Torsion Free

The authors extend and generalize some results of previous workers to ?-prime ?-ring. For a ?-square closed Lie ideal U of a 2-torsion free ?-prime ?-ring M, let d: M ?M be an additive mapping satisfying d(u?u)=d(u)? u + u?d(u) for all u ? U and ? ? ?. The present authors proved that d(u?v) = d(u)?v + u?d(v) for all u, v ? U and ?? ?, and consequently, every Jordan derivation of a 2-torsion free ?-prime ?-ring M is a derivation of M.Journal of Bangladesh Academy of Sciences, Vol. 39, No. 2, 249-255, 2015

scholarly journals Jordan Derivations on Completely Semiprime Gamma–Rings

2016 ◽  
Vol 34 ◽  
pp. 21-26
Author(s):  
Md Mizanor Rahman ◽  
Akhil Chandra Paul
Keyword(s):  
Semiprime Ring ◽  
Suitable Condition ◽  
Jordan Derivation ◽  
Gamma Rings ◽  
Torsion Free

In this paper we prove that under a suitable condition every Jordan derivation on a 2-torsion free completely semiprime ?-ring is a derivation.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 21-26

Equations arising from Jordan *-derivation pairs

2004 ◽  
Vol 67 (3) ◽  
pp. 236-240 ◽  
Author(s):  
Dijana Ilišević
Keyword(s):  
Jordan Derivation

The range of a Jordan *-derivation on an H *-algebra

1996 ◽  
Vol 72 (3) ◽  
pp. 261-267
Author(s):  
L. Moln�r
Keyword(s):  
Jordan Derivation
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