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JORDAN DERIVATIONS AND JORDAN LEFT DERIVATIONS OF BANACH ALGEBRAS

Communications of the Korean Mathematical Society, 2002
Summary: We obtain some results concerning Jordan derivations and Jordan left derivations mapping into the Jacobson radical. Our main result is the following: Let \(d\) be a Jordan derivation (resp. Jordan left derivation) of a complex Banach algebra \(A\). If \(d^2(x)=0\) for all \(x\in A\), then we have \(d(A)\subseteq\text{rad}(A)\).
Park, Kyoo-Hong, Jung, Yong-Soo
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Jordan {g,h}-derivations on triangular algebras

Open Mathematics, 2020
In this article, we give a sufficient and necessary condition for every Jordan {g,h}-derivation to be a {g,h}-derivation on triangular algebras. As an application, we prove that every Jordan {g,h}-derivation on τ(N)\tau ({\mathscr{N}}) is a {g,h ...
Kong Liang, Zhang Jianhua
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Characterization of Non-Linear Bi-Skew Jordan n-Derivations on Prime ∗-Algebras

Axioms, 2023
Let A be a prime *-algebra. A product defined as U•V=UV∗+VU∗ for any U,V∈A, is called a bi-skew Jordan product. A map ξ:A→A, defined as ξpnU1,U2,⋯,Un=∑k=1npnU1,U2,...,Uk−1,ξ(Uk),Uk+1,⋯,Un for all U1,U2,...,Un∈A, is called a non-linear bi-skew Jordan n ...
Asma Ali, Amal S. Alali, Mohd Tasleem
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ON JORDAN IDEALS AND JORDAN DERIVATIONS OF PRIME RINGS

Demonstratio Mathematica, 2004
A classical result by \textit{I. N. Herstein} [Proc. Am. Math. Soc. 8, 1104-1110 (1958; Zbl 0216.07202)] states that a Jordan derivation of a prime ring of characteristic not 2 is a derivation. The main result of the paper shows that the same is true on Jordan ideals of prime rings that are simultaneously subrings.
Ashraf, Mohammad, Nadeem-ur-Rehman
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Jordan's derivation of blackbody fluctuations [PDF]

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bacciagaluppi, G., Crull, Elise, Maroney, Owen   +2 more
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Jordan derivations of incidence algebras [PDF]

Rocky Mountain Journal of Mathematics, 2015
8 pages, to appear in Rocky Mountain J ...
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Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras

Special Matrices, 2018
Let R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module.
Alkenani Ahmad N., Ashraf Mohammad, Jabeen Aisha   +2 more
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A NOTE ON NONLINEAR MIXED ∗-JORDAN TYPE DERIVATIONS ON ∗-ALGEBRAS [PDF]

Journal of Algebraic Systems
Let S be a ∗-algebra containing the unity and a nontrivial projection. In the present paper, we showthat under certain restrictions if a map Ψ : S → S satisfies Ψ(L ⋄ N • D) = Ψ(L) ⋄ N • D + L ⋄Ψ(N) • D + L ⋄ N • Ψ(D) for all L, N, D ∈ S, then Ψ is an ...
Mohammad Siddeeque, Raof Ahmad Bhat, Abbas Hussain Shikeh   +2 more
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On Jordan mappings of inverse semirings

Open Mathematics, 2017
In this paper, the notions of Jordan homomorphism and Jordan derivation of inverse semirings are introduced. A few results of Herstein and Brešar on Jordan homomorphisms and Jordan derivations of rings are generalized in the setting of inverse semirings.
Shafiq Sara, Aslam Muhammad
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Generalized Derivations and Generalized Jordan Derivations on C∗-Algebras through Zero Products

Journal of Mathematics, 2022
Let A be a unital C∗-algebra and X be a unitary Banach A-bimodule. In this paper, we characterize continuous generalized derivations and generalized Jordan derivations as form D:A⟶X through the action on zero product.
Abbas Zivari-Kazempour, Abasalt Bodaghi
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