• 대한수학회논문집
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• 제9권2호
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• pp.299-302
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• 1994

Throughout this paper, let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$ /(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued (resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.(omitted)

• 대한수학회보
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• 제30권1호
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• pp.125-134
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• 1993

Let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued(resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.s.

• 대한수학회보
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• 제39권2호
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.65-72
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• 1998

We investigate a chain of properties of real function algebras along the analogous proofs of the complex cases such as the fact that any real function algebra which is both maximal and essential is pervasive. And some properties of real function algebras with a vertex property will be discussed.

• 충청수학회지
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• 제28권4호
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• pp.537-543
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• 2015

In [9], the authors determine an infinite class of non-unimodal Gorenstein sequence, which includes the example $$\bar{h}_1\text{ = (1, 125, 95, 77, 71, 77, 95, 125, 1)}$$. They raise a question whether there is a Gorenstein algebra with Hilbert function $$\bar{h}_2\text{= (1, 125, 95, 77, 70, 77, 95, 125, 1)}$$, which has remained an open question. In this paper, we prove that there is no Gorenstein algebra with Hilbert function $\bar{h}_2$.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.559-564
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• 2013

In this paper we investigate necessary conditions for the mirror algebra $(M(X),{\bigoplus},(0,0))$ to be a $d$-algebra (having the condition (D5), resp.) when (X, *, 0) is a d-algebra (having the condition (D5), resp.). Moreover, we obtain the necessary conditions for M(X) of a $d^*$-algebra X to be a $d^*$-algebra.

• 대한수학회논문집
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• 제10권1호
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• pp.123-131
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• 1995

The notion of our non-associative algebra is obtained from the Lotka-Volterra system of differential equation describing competitiion between animals or vegetals species and also in the kinetic theory of gasses. For the structure of an algebra, the existence of idempotents is of particular interest. But also from the biological aspect the existence of such elements is of interest because the equilibria of a population which can be described by an algebra correspond to idempotents of this algebra. Thus we present some properties of the general natures for a Lotka-Volterra algebra associated to a weight function and idempotents elements.

• 충청수학회지
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• 제25권2호
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• pp.319-329
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• 2012

For a norm 1 function ${\sigma}$ in the Fourier-Stieltjes algebra of a locally compact group we define the space of ${\sigma}$-harmonic operators in the non-commutative $L^p$-space associated to the group von Neumann algebra of G. We will investigate some properties of the space and will obtain a precise description of it.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.615-625
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• 2018

In this paper, we discuss the connection between the 5-dimensional complex Lie algebra ${\mathcal{K}} _5$ and Special functions. We construct certain two variable models of the irreducible representations of ${\mathcal{K}}_5$. We also use an Euler type integral transformation to obtain the new transformed models, in which the basis function appears as $_2F_1$. Further, we utilize these models to get some generating functions and recurrence relations.

• 충청수학회지
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• 제33권4호
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• pp.497-504
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• 2020

A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.