• Honam Mathematical Journal
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• v.20 no.1
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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.

• The Pure and Applied Mathematics
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• v.5 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.235-247
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• 2012

We study sufficient conditions for function algebras generated by four smooth functions on a small closed bidisk near the origin in $\mathbb{C}$ to coincide with the space of continuous functions on the bidisk. This problem in one dimension has been studied by De Paepe and the second name author.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.753-761
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• 2007

In this note we extend the results of [3] concerning subadditive separating maps from A=C(X) to B=C(Y), for compact Hausdorff spaces X and Y, to the case where A and B are regular Banach function algebras(not necessarily unital) with A satisfying Ditkin#s condition. In particular we describe the general form of these maps and get a result on continuity of separating linear functionals.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.629-636
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• 1999

We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.501-510
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• 2020

This paper considers coupled fixed point theorems on unital without of order semi-simple fundamental locally multiplicative topological algebras (abbreviated by FLM algebras).

• Honam Mathematical Journal
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• v.22 no.1
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• pp.21-30
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• 2000

Lipschitz Algebras Lip(X, ${\alpha}$) and lip(X, ${\alpha}$) were first studied by D. R. Sherbert in 1964. B. Pavlovic in 1995 shown that in these algebras, the prime ideals containing a given prime ideal form a chain. In this paper, we show that the above property holds in $Lip^n(X,\;{\alpha})$ and $lip^n(X,\;{\alpha})$, the Lipschitz algebras of finite differentiable functions on a perfect compact place set X.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.117-125
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• 2020

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.147-153
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• 2009

In this paper, we give some constructions of implicative/commutative d-algebras which are not BCK-algebras. This demonstrate that the notion of implicative/commutative d-algebras are indeed generalizations of the same in BCK-algebras.