• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.37-44
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• 1995

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 zero.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.113-124
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• 2006

In this article, we show that for an approximate derivation on a Banach *-algebra, there exist a unique derivation near the an approximate derivation and for an approximate derivation on a $C^*$-algebra, there exist a unique derivation near the approximate derivation.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.65-69
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• 1993

In this paper, we show that the module derivation D is continuous on the Banach algebra and the Silov algebra, and also that the derivation restricted by separating space and the radical on the semi prime Banach algebra is continuous.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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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.

• Journal of applied mathematics & informatics
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• v.4 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.367-372
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• 1995

In 1955 Singer and Wermer [12] proved that every bounded derivation on a commutative Banach algebra maps into its radical. They conjectured that the continuity of the derivation in their theorm can be removed. In 1988 Thomas [13] proved their conjecture ; Every derivation on a commutative Banach algebra maps into its radical. For noncommutative versions, in 1984 B. Yood [15] proved that the continuous derivations on Banach algebras satisfing [D(a),b] $\in$ Rad(A) for all a, b $\in$ A have the radical range, where [a,b] will be denote the commutator ab-ba. In 1990 M.Bresar and J.Vukman [1] have generlized Yood's result, that is, the continuous linear Jordan derivation on Banach algebra that satisfies [D(a),a] $\in$ Rad(A) for all a $\in$ A has the radical range. In next year Mathieu and Murphy [5] proved that every bounded centralizing derivation on Banach algebras has its image in the radical. Mathieu and Runde [6] removed the boundedness of that.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.195-205
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• 2019

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.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.31-34
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• 1989

In this paper we show that if there is a derivation on a commutative Banach algebra which has a non-nilpotent separating space, then there is a discontinuous derivation on a commutative Banach algebra which has a range in its radical. Also we show that if every prime ideal is closed in a commutative Banach algebra with identity then every derivation on it has a range in its radical.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.477-481
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• 1999

Every spectrally bonded Jordan derivation on a unital Banach algebra maps into its Jacobson radical.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.489-499
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• 1998

Let A be the non-commutative Banach algebra with identity satisfying certain conditions. We show that if D is a derivation on A, then D(A) is contained in the radical of A.