• Journal of applied mathematics & informatics
• /
• 제6권2호
• /
• pp.611-630
• /
• 1999

In this paper we show that the Derivation D(A) on the non-commutative Banach algebra A with identity satisfying certain conditions is contained in the radical of A and will show some examples satisfying such properties.

• 충청수학회지
• /
• 제23권3호
• /
• pp.563-570
• /
• 2010

In this article, we take account of the fuzzy stability for generalized derivation in fuzzy Banach algebra.

• Journal of applied mathematics & informatics
• /
• 제7권1호
• /
• pp.305-317
• /
• 2000

It is well-known that every derivation on a commutative Banach algebra maps into its radical. In this paper we shall give the various algebraic conditions on the ring that every Jordan derivation on a noncommutative ring with suitable characteristic conditions is zero and using this result, we show that every continuous linear Jordan derivation on a noncommutative Banach algebra maps into its radical under the suitable conditions.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.57-64
• /
• 2022

In this paper, we show, among others, that if A is a Banach algebra satisfying a functional identity involving a b-generalized derivation F on A, under some mild conditions, is of the form F(x) = ax for all x ∈ R, where a ∈ Q_r, a right Martindale quotient ring of A.

• 대한수학회보
• /
• 제37권2호
• /
• pp.265-272
• /
• 2000

Let D be a derivation on an Banach algebra A. Suppose that [[D(x), x], D(x)] lies in the nil radical of A for all $x{\;}{\in}{\;}A$. Then D(A) is contained in the Jacobson radical of A.

• 대한수학회보
• /
• 제33권3호
• /
• pp.359-366
• /
• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• 대한수학회보
• /
• 제38권3호
• /
• pp.443-447
• /
• 2001

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.

• 대한수학회보
• /
• 제35권3호
• /
• pp.583-590
• /
• 1998

The purpose of this paper is to prove the following results: Let A be a noncommutative semisimple Banach algebra. (1) Suppose that a linear derivation D : A $\to A$ is such that [D(x),x]x=0 holds for all $x \in A$. Then we have D=0. (2) Suppose that a linear derivation $D:A\to A$ is such that $D(x)x^2 + x^2D(x)=0$ holds for all $x \in A$. Then we have C=0.

• 대한수학회보
• /
• 제47권1호
• /
• pp.151-157
• /
• 2010

In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\delta$ be a spectrally bounded left Jordan derivation on a Banach algebra A. Then $\delta$ maps A into its Jacobson radical. (ii) Let $\delta$ be a left Jordan derivation on a unital Banach algebra A with the condition sup{r$(c^{-1}\delta(c))$ : c $\in$ A invertible} < $\infty$. Then $\delta$ maps A into its Jacobson radical. Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in [2, p. 260]: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation.

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.425-432
• /
• 2003

Our main goal is to show that if there exists a continuous linear Jordan derivation D on a noncommutative Banach algebra A such that n$^{x}$ D(x)n+xD(x)x$^{n}$ $\in$ rad(A) for all x $\in$ A, then D maps A into rad(A).