• 충청수학회지
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• 제20권4호
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• pp.367-373
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• 2007

For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.

• 호남수학학술지
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• 제17권1호
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• 대한수학회논문집
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• 제35권3호
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• pp.733-744
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• 2020

Let 𝕽 be a commutative ring with unity, A and B be 𝕽-algebras, M be a (A, B)-bimodule and N be a (B, A)-bimodule. The 𝕽-algebra 𝕾 = 𝕾(A, M, N, B) is a generalized matrix algebra defined by the Morita context (A, B, M, N, 𝝃_MN, Ω_NM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• 대한수학회논문집
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• 제35권4호
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• pp.1159-1170
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• 2020

We consider the weighted spaces ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓ^p(𝕊, 𝜓) to be multiplier weighted-space of ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓ^p(ℤ,𝜓) is a convolutive algebra.

• 한국통신학회논문지
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• 제30권1C호
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• pp.1-8
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• 2005

본 논문에서는 이중 대각 부행렬에 근거한 결정적 LDPC 부호의 일종인 반집합 대수 LDPC 행렬이라는 새로운 LDPC 부호의 구성을 제시한다. 이러한 구성 방법에 의해 일종의 high rate LDPC 부호를 얻게 되며, 이 부류의 부호들은 큰 girth와 양호한 최소거리 특성을 갖는다. 또한, 순환 시프트 레지스터를 이용한 단순한 병렬 어레이 구조로 구현할 수 있으며, 반복 복호에 의해 용이하게 처리될 수 있다.

• 대한수학교육학회지:학교수학
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• 제9권1호
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• pp.141-160
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• 2007

본 연구의 목적은 대수 문장제를 해결하기 위하여 학생들이 이전지식이나 경험을 어떻게 적용하는가를 조사하고자 학생들의 풀이과정에 대한 유사성을 일련의 표시(chain of signification) 관점에서 분석하는 것이다. 이를 위하여 본 연구에서는 중학생 3명을 대상으로 사례 연구를 실시하였다. 연구 결과, 학생A나 학생C는 (반)열린 공식을 해법 원리로 생각하여 구체화하는 과정을 일련의 표시로 구성하였다. 학생A와 학생C는 문제를 읽으면서 숫자 정보와 텍스트를 기반으로 정신적 모델을 구성하였으며, 그 의미(기의)와 기록(기표) 과정을 점진적으로 구성함으로써 일련의 표시 과정을 구성하였다. 학생A의 표시과정은 숫자나 문자, 그리고 그리기가 혼합된 것이었다. 그러나 학생C와 학생B는 단지 숫자나 문자만으로 구성하였다. 특히, 학생B는 특정한 문제정보만을 근거로 그 상황을 생각하지 않고, 자신의 알고리즘을 적용하기 위하여 자신이 구성한 규칙을 적용하고자 하는 시행착오에 대한 유사성을 구성하였다.

• 대한수학회논문집
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• 제35권2호
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.167-173
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• 2004

Given vectors x and y in a separable Hilbert space $\cal H$, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate Hilbert-Schmidt interpolation problems for vectors in a tridiagonal algebra. We show the following: Let $\cal L$ be a subspace lattice acting on a separable complex Hilbert space $\cal H$ and let x = ($x_{i}$) and y = ($y_{i}$) be vectors in $\cal H$. Then the following are equivalent; (1) There exists a Hilbert-Schmidt operator A = ($a_{ij}$ in Alg$\cal L$ such that Ax = y. (2) There is a bounded sequence {$a_n$ in C such that ${\sum^{\infty}}_{n=1}\mid\alpha_n\mid^2 < \infty$ and $y_1 = \alpha_1x_1 + \alpha_2x_2$ ... $y_{2k} =\alpha_{4k-1}x_{2k}$ $y_{2k=1} = \alpha_{4kx2k} + \alpha_{4k+1}x_{2k+1} + \alpha_{4k+1}x_{2k+2}$ for K $\epsilon$ N.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.401-406
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• 2008

Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX=Y. In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following: Let ${\pounds}$ be a subspace lattice acting on a separable complex Hilbert space H and let X=$(x_{ij})$ and Y=$(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator $A=(a_{ij})$ in Alg${\pounds}$ such that AX=Y. (2) There is a bounded sequence $\{{\alpha}_n\}$ in $\mathbb{C}$ such that ${\sum}_{n=1}^{\infty}|{\alpha}_n|^2<{\infty}$ and $$y1_i={\alpha}_1x_{1i}+{\alpha}_2x_{2i}$$ $$y2k_i={\alpha}_{4k-1}x_2k_i$$ $$y{2k+1}_i={\alpha}_{4k}x_{2k}_i+{\alpha}_{4k+1}x_{2k+1}_i+{\alpha}_{4k+2}x_{2k+2}_i\;for\;all\;i,\;k\;\mathbb{N}$$.