• 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.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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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.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.591-603
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• 2005

A representation for non-commutative Banach algebras is discussed, which generalizes the Gelfand representation for commutative Banach algebras and the Gelfand-Naimark representation for $C^{\ast}$-algebras. Its basic properties are also investigated. In appendix, an example of Banach algebra that is neither semi-simple nor radical is presented.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.649-655
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• 2005

The universal mapping property and the Gelfand- Kirillov dimension of a skew enveloping algebra are studied and it is proved that every Poisson enveloping algebra is a homomorphic image of a skew enveloping algebra.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.527-538
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• 2014

Let K be a compact Hausdorff space, $\mathfrak{A}$ a commutative complex Banach algebra with identity and $\mathfrak{C}(\mathfrak{A})$ the set of characters of $\mathfrak{A}$. In this note, we study the class of functions $f:K{\rightarrow}\mathfrak{A}$ such that ${\Omega}_{\mathfrak{A}}{\circ}f$ is continuous, where ${\Omega}_{\mathfrak{A}}$ denotes the Gelfand representation of $\mathfrak{A}$. The inclusion relations between this class, the class of continuous functions, the class of bounded functions and the class of weakly continuous functions relative to the weak topology ${\sigma}(\mathfrak{A},\mathfrak{C}(\mathfrak{A}))$, are discussed. We also provide some results on its completeness under the norm defined by ${\mid}{\parallel}f{\parallel}{\mid}={\parallel}{\Omega}_{\mathfrak{A}}{\circ}f{\parallel}_{\infty}$.

• Communications of the Korean Mathematical Society
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• v.7 no.1
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• pp.33-36
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• 1992

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.109-115
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• 1993

In 1940 Eidelheit showed that every homomorphism of a Banach algebra onto the Banach algebra B(X) of all bounded linear operators on a Banach space X is continuous. At about the same time, Gelfand proved that every homomorphism of a commutative Banach algebra into a commutative semi-simple Banach algebra is continuous. In [7] Johnson proved that every homomorphism of a Banach algebra onto non-commutative semi-simple Banach algebra is continuous, and this is still the most important result of this type. In this paper we are concerned with continuity of derivations on commutative Banach algebras and of homomorphisms into commutative Banach algebras. Throughout this paper we suppose that A is a commutative Banach algebra. R will denote the redical of A.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1185-1195
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• 2007

We will discuss some very old and some new open problems concerning infinite dimensional algebras. All these problems have been inspired by combinatorial group theory.