• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.33-41
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• 1988

In this paper, the abelian property of Hermitian elements holds not generally in Banach algebra, but in the case that some conditions satisfy, they are abelian. By using property of [1], [2], the Hermitian elements a and b in Banach algebras have been shown that ab = ba.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.165-170
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• 2018

In this paper, we show that every unital n-Jordan homomorphism ${\varphi}$ from a Banach algebra ${\mathcal{A}}$ onto a semisimple commutative Banach algebra B is continuous.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.543-551
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• 2011

In this paper, we consider the functional inequalities with approximately centralizing derivations on noncommutative Banach algebras, and investigate the problem that functions satisfying the functional inequalities mentioned above map into the radical.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.57-64
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• 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.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.299-308
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• 1997

In this paper we show that the limit of a convergent in-vertible sequence in the set of invertible elements Inv(A) in a Banach algebra A under a certain conditions is invertible and we investigate some properties of the spectral radius of banach algebra with unit.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.319-327
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• 2000

In this paper we investigate the conditions for derivations under which the Singer-Wermer theorem is true for noncommutative Banach algebra A such that either [[D(x),xD(x)] ${\in}$ rad(A) for all $x{\in}$A or $D(x)^2$x+xD(x))$^2$${\in}$rad(A) for all $x{\in}$A, where rad(A) is the Jacobson radical of A, then $D(A){\subseteq}$rad(A).

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.187-191
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• 1999

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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.265-272
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• 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.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.135-147
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• 2018

Lu et al. [27] defined derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the definitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the definitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.89-94
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• 1993

The main goal of the present paper is to investigate conditions for the separating ideal of a Banach algebra to be nilpotent.