• 대한수학회보
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• 제25권2호
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• pp.179-183
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• 1988

In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.

• 대한수학회논문집
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• 제33권3호
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• pp.721-739
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• 2018

In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).

• 호남수학학술지
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• 제36권4호
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• pp.907-911
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• 2014

Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following: Let $Alg{\mathcal{L}}$ be a tridiagonal algebra on $\mathcal{H}$ and let $x=(x_i)$ and $y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that Ax = y. (2) There is a bounded sequence $\{{\alpha}_i\}$ in $\mathbb{C}$ such that ${\mid}{\alpha}_i{\mid}=1$ and $y_i={\alpha}_ix_i$ for $i{\in}\mathbb{N}$.

• 대한수학회논문집
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• 제37권2호
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• pp.327-335
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost weakly finite conductor if for any two elements a and b in R, there exists a positive integer n such that aⁿR ∩ bⁿR is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of nonfinite conductor weakly finite conductor rings.

• 대한수학회논문집
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• 제38권4호
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• pp.1101-1110
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• 2023

At the present paper, we investigate bounded approximately local derivations of ℓ¹-Munn algebra 𝕄_I(𝒜), where I is an arbitrary non-empty set and 𝒜 is an approximately locally unital Banach algebra. Indeed, we show that if _𝒜B(𝒜, 𝒜^*) and B_𝒜(𝒜, 𝒜^*) are reflexive, then every bounded approximately local derivation from 𝕄_I(𝒜) into any Banach 𝕄_I(𝒜)-bimodule X is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra ℓ¹(S), where S is a uniformly locally finite inverse semigroup.

• 대한수학회지
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• 제41권6호
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• pp.945-955
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• 2004

In this paper, we establish a number system in $R^n$ which arises from a Haar wavelet basis in connection with decompositions of certain Cuntz algebra representations on $L^2$( $R^n$). Number systems in $R^n$ are also of independent interest [9]. We study radix-representations of $\chi$ $\in$ $R^n$: $\chi$:$\alpha$$_{ι}$ $\alpha$$_{ι-1}$…$\alpha$$_1$$\alpha$$_{0}$ ㆍ$\alpha$$_{-1}$ $\alpha$$_{-2}$ … as $\chi$= $M^{ι}$$\alpha$$_{ι}$ $\alpha$＋…M$\alpha$$_1$＋$\alpha$$_{0}$ ＋ $M^{-1}$ $\alpha$$_{-1}$ ＋ $M^{-2}$ $\alpha$$_{-2}$ ＋… where each $\alpha$$_{k}$ $\in$ D, and D is some specified digit set. Our analysis uses iteration techniques of a number-theoretic flavor. The view-point is a dual one which we term fractals in the large vs. fractals in the small,illustrating the number theory of integral lattice points vs. fractions.s vs. fractions.

• 대한수학회보
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• 제36권4호
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• pp.717-722
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• 1999

The set of continuous maps of a space X to real usual space R equipped with the toplogy of pointwise convergence will be denoted by $C_p$(X). In this paper, we prove that; $C_p$(X) is hereditarily separable and hereditary Lindelof if and only if $X^n$ is hereditarily separable and hereditary Lindelof.

• 대한수학회지
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• 제32권4호
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• pp.689-695
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• 1995

Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.223-230
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• 2007

We give an answer to the following question: Question. Let S be a subset of [0,1] containing a maximal element m > 0 and let C :=$\{I_{t}\;{\mid}\;t{\in}S\}$ be a decreasing chain of ideals of a BCK/BCI-algebra X. Then does there exists a fuzzy ideal ${\mu}(X)=S\;and\;C_{\mu}=C?$.

• 충청수학회지
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• 제3권1호
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• pp.41-48
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• 1990

Let D' : $C^n$[0, 1] ${\rightarrow}$ M be a second order derivation from the Banach algebra of n times continuously differentiable functions on [0, 1] into a Banach $C^n$[0, 1]-module M and let D be the primitive of D'. If D' is continuous and D'(z) lies in the 1-differential subspace, then it is completely determined by D(z) and D'(z) where z(t)=t, $0{\leq}t{\leq}1$.