• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.689-697
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• 2022

In this paper, we study dual integrable representations of locally compact commutative hypergroups and give a sufficient and necessary condition for a dual integrable representation to have an admissible vector.

• 대한수학회지
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• 제50권1호
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• pp.161-171
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• 2013

Given an integer $n{\geq}1$ and a compact group G, we find some restrictions for the probability that two randomly picked elements $x^n$ and $y$ of G commute. In the case $n=1$ this notion was investigated by W. H. Gustafson in 1973 and its influence on the structure of the group has been studied in the researches of several authors in last years.

• 대한수학회지
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• 제56권1호
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• pp.53-65
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• 2019

Recently, Chung and Lee [2] introduced the notion of topological stability for a finitely generated group action, and proved a group action version of the Walters's stability theorem. In this paper, we introduce the concepts of continuous shadowing and continuous inverse shadowing of a finitely generated group action on a compact metric space X with respect to various classes of admissible pseudo orbits and study the relationships between topological stability and continuous shadowing and continuous inverse shadowing property of group actions. Moreover, we introduce the notion of structural stability for a finitely generated group action, and we prove that an expansive action on a compact manifold is structurally stable if and only if it is continuous inverse shadowing.

• 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).

• 대한수학회논문집
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• 제9권2호
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• pp.415-418
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• 1994

Let G be a compact Lie group and let $S^1$ denote the unit circle in $R^2$ with the standard metric. Since every smooth compact Lie group action on $S^1$ is smoothly equivalent to a linear action (cf. [3J TH 2.0), we may think of $S^1$ with a smooth G-action as S(V) the unit circle of a real 2-dimensional orthogonal G-module V.(omitted)

• 대한수학회보
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• 제36권4호
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• pp.755-762
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• 1999

Let X be a p-compace groyp, Y -> X bd a p-compact-subgroup of X and G -> X be a p-compact toral subgroup of X with $(X/Y)^{hG} \neq 0$. In this paper we show that the homotopy fixed point set of the homotopy fibre $(X/Y)^{hG}$ is $F_p$-finite.

• 대한수학회보
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• 제55권4호
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• pp.1125-1135
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• 2018

We show that for an M-action on a compact Hausdorff uniform space, if it has at least two disjoint compact invariant subsets, then it is thickly syndetically sensitive. Additionally, we point out that for a P-M-action of a discrete abelian group on a compact Hausdorff uniform space, the multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity.

• 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.

• 대한수학회보
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• 제54권1호
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• pp.71-84
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• 2017

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.

• 대한수학회지
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• 제36권2호
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• pp.243-256
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• 1999

We will consider f,g : S1longrightarrowS2 a pair of maps between two orientable compact surfaces. The purpose of this paper is to decide when the pair can be deformed to a pair (f', g') such that