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ALMOST QUADRATIC LIE *-DERIVATIONS ON CONVEX MODULAR *-ALGEBRAS
ICK-SOON CHANG,HARK-MAHN KIM 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
In this article, we investigate an approximate quadratic Lie $\ast$-derivationof a quadratic functional equation$$f(a x + b y)+ ab f(x -y) = (a+b) ( a f(x) + b f( y) ), $$where $ a b \ne 0, \ a, b \in \mathbb{N},$associated with the identity $f( [x, y] ) = [f(x), y^2] + [x^2 , f(y)]$on a $\rho$-complete convex modular $\ast$-algebra $\chi_\rho$ by using $\Delta_2$-condition via convex modular $\rho.$
Chang, Ick-Soon 충청수학회 1999 충청수학회지 Vol.12 No.1
In this paper we will show that if [G(y), x]D(x) lies in the nil radical of A for all $x{\in}A$, then GD maps A into the radical, where D and G are derivations on a Banach algebra A.
A RESULT CONCERNING DERIVATIONS IN NONCOMMUTATIVE BANACH ALGERAS
Chang, Ick-Soon 충청수학회 1997 충청수학회지 Vol.10 No.1
The purpose of this paper is to prove the following result: Let A be a noncommutative semisimple Banach algebra. Suppose that $D:A{\rightarrow}A$, $G:A{\rightarrow}A$ are linear derivations such that [G(x), x]D(x) = D(x)[G(x), x] = 0, [D(x), G(x)] = 0 hold for all $x{\in}A$. In this case either D = 0 or G = 0.
Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
Chang, Ick-Soon,Alizadeh, Badrkhan,Gordji, M. Eshaghi,Kim, Hark-Mahn SPRINGER SCIENCE AND BUSINESS MEDIA 2015 MATHEMATICA SLOVACA Vol.65 No.1
<P><B>Abstract</B></P><P>In this paper, we prove the stability of higher ring derivations associated with a general Cauchy-Jensen functional inequality in the class of mappings from non-Archimedean normed algebras to non-Archimedean Banach algebras.</P>
A RESULT OF LINEAR JORDAN DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS
Chang, Ick-Soon 충청수학회 1998 충청수학회지 Vol.11 No.1
The purpose of this paper is to prove the following result: Let A be a noncom mutative Banach algebra. Suppose that $D:A{\rightarrow}A$ is a continuous linear Jordan derivation such that $D^2(x)D(x)^2{\in}rad(A)$ for all $x{\in}A$. Then D maps A into its radical.
APPROXIMATE LINEAR MAPPING OF DERIVATION-TYPE ON BANACH ∗-ALGEBRA
Chang, Ick-Soon Chungcheong Mathematical Society 2019 충청수학회지 Vol.32 No.2
We consider additive mappings similar to derivations on Banach ${\ast}$-algebras and we will first study the conditions for such additive mappings on Banach ${\ast}$-algebras. Then we prove some theorems concerning approximate linear mappings of derivation-type on Banach ${\ast}$-algebras. As an application, approximate linear mappings of derivation-type on $C^{\ast}$-algebra are characterized.
JORDAN DERIVATIONS IN NONCOMMUTATIVE BANACH ALGEBRAS
Chang, Ick-Soon Korean Mathematical Society 2000 대한수학회보 Vol.37 No.3
Our main goal is to show that if there exist Jordan derivations D, E and G on a noncommutative 2-torsion free prime ring R such that$(G^2(x)+E(x))D(x)=0\ or\ D(x)(G^2(x)+E(x))=0\ for\ all\ x\inR$, then we have D=o or E=0, G=0.
DERIVATIONS ON NONCOMMUTATIVE SEMI-PRIME PINGS
Chang, Ick-Soon,Byun, Sang-Hoon 한국전산응용수학회 1999 Journal of applied mathematics & informatics Vol.6 No.1
The purpose of this paper is to prove the following result: Let R be a 2-torsion free noncommutative semi-prime ring and D:RlongrightarrowR a derivation. Suppose that $[[D(\chi),\chi],\chi]\in$ Z(R) holds for all $\chi \in R$. Then D is commuting on R.
A RESULT OF LINEAR JORDAN DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS
ICK SOON CHANG 충청수학회 1998 충청수학회지 Vol.11 No.1
The purpose of this paper is to prove the following result: Let A be a noncommutative Banach algebra. Suppose that D : A → A is a continuous linear Jordan derivation such that D²(x)D(x)² ∊ rad(A) for all x ∊ A. Then D maps A into its radical.