• 대한수학회보
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• 제45권1호
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• pp.111-118
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• 2008

Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)$$=f(x)+f(y)+2f(z), which was introduced and investigated in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.

• 호남수학학술지
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• 제20권1호
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• pp.79-88
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• 1998

In this paper we define the concept of $Fr{\acute{e}}chet$ function algebras on hemicompact spaces. So we show that under certain condition they can be represented as a projective limit of Banach function algebras. Then the class of $Fr{\acute{e}}chet$ Lipschitz algebras on hemicompact metric spaces are defined and their relations with the class of lipschitz algebras on compact metric spaces are studied.

• 대한수학회보
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• 제36권4호
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• pp.737-746
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• 1999

For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.171-180
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• 2018

In this paper, the necessary and sufficient conditions are considered for biprojectivity of Banach algebras $E_p(I)$. As an application, we investigate biprojectivity of convolution Banach algebras A(G) and $L^2(G)$ on a compact group G.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권2호
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• pp.91-102
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• 2021

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

• East Asian mathematical journal
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• 제17권1호
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• pp.33-45
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• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.

• 호남수학학술지
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• 제27권1호
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• pp.77-82
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• 2005

$C^*$-algebras which are closed sub-algebras of Banach algebras have been studied many years ago. In this note we extend the main definition of $C^*$-algebras to metrizable topological algebras.

• 대한수학회보
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• 제32권2호
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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.

• 호남수학학술지
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• 제42권1호
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• pp.37-48
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• 2020

We first define a new multiplication on triangular Banach algebras. Then we study amenability, weak amenability, biflatness and biprojectivity of these algebras.

• 호남수학학술지
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• 제42권4호
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• pp.757-768
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• 2020

In this paper, the Hyers-Ulam-Rassias stability of mixed n-Jordan homomorphisms on Banach algebras and the superstability of mixed n-Jordan ∗-homomorphism between C∗-algebras are investigated.