• 대한수학회보
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• 제38권4호
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• pp.709-718
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• 2001

In this paper we show that if D and G are continuous linear Jordan derivations on a Banach algebra A satisfying [D(x), x]x - x[G(x),x] $\epsilon$ rad(A)for all $\epsilon$ A, then both D and G map A into rad(A).

• 충청수학회지
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• 제4권1호
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• pp.91-97
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• 1991

This paper studies the structure and continuity of derivations of the Banach algebra $C^n(I)$ of n times continuously differentiable functions on an interval I into Banach $C^n(I)$-modules.

• 대한수학회보
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• 제37권3호
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• pp.429-435
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• 2000

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.

• 대한수학회논문집
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• 제23권3호
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• pp.387-399
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• 2008

We investigate approximately higher ternary derivations in Banach ternary algebras via the Cauchy functional equation $$f({\lambda}_{1x}+{\lambda}_{2y}+{\lambda}_{3z}={\lambda}_1f(x)+{\lambda}_2f(y)+{\lambda}_3f(z)$$.

• 대한수학회보
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• 제35권4호
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• pp.659-667
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• 1998

In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the Jacobson radical of A, and hence every left derivation on a semisimple Banach algebra is always zero.

• 대한수학회보
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• 제38권3호
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• pp.443-447
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• 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.

• 대한수학회논문집
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• 제14권1호
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• pp.69-74
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• 1999

In [2], the author discusses derivations of A(p,q) when A(p,q) is prime and p,q $\in$ A satisfy the condition A=Ap+Aq+R where R is a subspace of Z(A). In this paper, we consider a general-ization of Theorem 1 in [2] for the semiprime case of A(p,q).

• 대한수학회보
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• 제46권2호
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• pp.347-358
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• 2009

In [8], the author decomposed the Dirichlet form associated to a bounded generator G of a $weakly^*$-continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M. The aim of this paper is to extend G to the unbounded generator using the bimodule structure and derivations.

• 충청수학회지
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• 제22권4호
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• pp.615-622
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• 2009

We solve the automatic continuity problem of an approximate higher derivation on a semisimple Banach algebra and investigate Hyers-Ulam stability for higher derivations.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.263-271
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• 1997

In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the jacobson radical of A and hence every left derivation on a semisimple Banach algebra is always zero.