• 호남수학학술지
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• 제34권2호
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• pp.289-295
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• 2012

In this note we prove the space (A, ${\parallel}.{\parallel}$) is a Banach space and ${\parallel}ab{\parallel}{\leq}{\parallel}a{\parallel}{\parallel}b{\parallel}$ for $a,b{\in}A$ where $A:=\{a:=(a_t)_{t{\in}G}:{\sum}_{t{\in}G}{\parallel}a_t{\parallel}_t<{\infty}\}$, $G=\mathbb{N}^*$. Also we show some property in (A, ${\parallel}.{\parallel}$).

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.889-893
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• 1998

In this paper we show that $\sigma$a maps into the radical if and only if for every irreducible representation $\pi$,$\pi$(a) is scalar and obtain that every inner derivation corresponding to $\sigma$-quasi central elements in some Banach algebra maps into the radical.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.107-119
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• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

• 충청수학회지
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• 제24권2호
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• pp.337-344
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• 2011

We provide another unified proof that $A_{\gamma}(G)$ and $A_{\Delta}(G)$ are Banach algebras for a compact group G, where $A_{\gamma}(G)$ and $A_{\Delta}(G)$ are images of the convolution and the twisted convolution, respectively, on $A(G{\times}G)$. Our new approach heavily depends on analysis of co-multiplication on VN(G), the group von-Neumann algebra of G.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.491-502
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• 2022

In this paper we investigate some sufficient conditions to guarantee the existence and uniqueness of Stepanov-like weighted pseudo almost periodic solutions of cellular neural networks on Clifford algebra for non-automomous cellular neural networks with multi-proportional delays. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.521-536
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• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• 대한수학회보
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• 제47권2호
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• pp.307-317
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• 2010

In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and $L^2(K)$ for a compact hypergroup K, together with their applications to convolution Banach algebras $L^p(K)$ ($2\;{\leq}\;p\;<\;{\infty}$). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

• 충청수학회지
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• 제37권1호
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• pp.19-26
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• 2024

In this paper, we investigate the properties related to algebraic spectral subspaces and divisible subspaces of linear operators on a Banach space. In addition, using the concept of topological divisior of zero of a Banach algebra, we prove that the only closed divisible subspace of a bounded linear operator on a Banach space is trivial. We also give an example of a bounded linear operator on a Banach space with non-trivial divisible subspaces.

• 대한수학회논문집
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• 제12권4호
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• pp.911-920
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• 1997

This note centers around the class M(A) of multipliers on a Gelfand algebra A. This class is a large subalgebra of the Banach algebra L(A). The aim of this note is to investigate some aspects concerning their local spectral properties of multipliers. In the last part of work we consider some applications to automatic continuity theory.

• 대한수학회논문집
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• 제26권2호
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• pp.253-259
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• 2011

Let A and B be Banach algebras with unit. Here we prove that an approximate algebra homomorphism f : A ${\rightarrow}$ B, in the sense of Rassias, is an algebra homomorphism.