• 충청수학회지
• /
• 제23권1호
• /
• pp.149-161
• /
• 2010

We adopt the idea of $C{\breve{a}}dariu$ and Radu to prove the generalized Hyers-Ulam stability of generalized Jordan triple derivation in Banach algebra. In addition, we take account of problems for generalized Jordan triple linear derivation in Banach algebra.

• 대한수학회논문집
• /
• 제13권3호
• /
• pp.489-499
• /
• 1998

Let A be the non-commutative Banach algebra with identity satisfying certain conditions. We show that if D is a derivation on A, then D(A) is contained in the radical of A.

• Journal of applied mathematics & informatics
• /
• 제6권2호
• /
• pp.611-630
• /
• 1999

In this paper we show that the Derivation D(A) on the non-commutative Banach algebra A with identity satisfying certain conditions is contained in the radical of A and will show some examples satisfying such properties.

• 대한수학회지
• /
• 제32권4호
• /
• pp.775-784
• /
• 1995

Let $H$ be a separable, infnite dimensional, complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$.

• 대한수학회논문집
• /
• 제9권4호
• /
• pp.847-852
• /
• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operator on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$.

• 대한수학회지
• /
• 제35권1호
• /
• pp.237-257
• /
• 1998

By introducing the notion of a generalized normal state space, we give a necessary and sufficient condition for that there exists a unital normal completely map from a von Neumann algebra into another, in terms of their generalized normal state spaces.

• 한국수학교육학회지시리즈E:수학교육논문집
• /
• 제30권1호
• /
• pp.1-22
• /
• 2016

본 연구에서는 문헌 및 사례 분석을 통해 효과적인 플립드러닝 강의 모델을 모색해 보고, 그간 대학에서의 '선형대수학' 강좌를 위하여 시도한 다양한 플립드러닝 강의 경험을 정리하여 '선형대수학' 강의 모델을 개발하고 실제 강의 현장에 적용해 플립드러닝의 효과를 연구자의 입장에서 뿐만 아니라 학습자의 관점에서도 그 과정과 결과를 분석하며 검증하였다. 그 결과, 플립드러닝은 학생들이 미리 온라인 동영상 강의를 듣고 수업에 참여하므로 다양한 학습자 중심의 활동으로 구성이 가능하며, 따라서 수학적 지식 습득에 성취감을 고취시킬 뿐 아니라 학생들의 참여도와 자신감 그리고 도전의욕 증가에 유의미한 영향을 준 것을 충분한 데이터와 설문조사를 최신 통계기법을 활용하여 분석함으로 확인하였다.

• 충청수학회지
• /
• 제23권1호
• /
• pp.49-57
• /
• 2010

It is shown that for a derivation $$f(x_1{\cdots}x_{j-1}x_jx_{j+1}{\cdots}x_k)=\sum_{j=1}^{k}x_{1}{\cdots}x_{j-1}x_{j+1}{\cdots}x_kf(x_j)$$ on a unital $C^*$-algebra $\mathcal{B}$, there exists a unique $\mathbb{C}$-linear *-derivation $D:{\mathcal{B}}{\rightarrow}{\mathcal{B}}$ near the derivation, by using the Hyers-Ulam-Rassias stability of functional equations. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회 1993년도 추계학술대회발표논문집; 서강대학교, 서울; 25 Sep. 1993
• /
• pp.118-118
• /
• 1993

We consider a discrete event dynamic system called periodic job shop, where an identical mixture of items called minimal part set(MPS) is repetitively produced in the same processing order and the primary performance measure is the cycle time. The precedence relationships among events(starts of operations) are represented by a directed graph with rocurront otructure. When each operation starts as soon as all its preceding operations complete(called earliest starting), the occurrences of events are modeled in a linear system using a special algebra called minimax algebra. By investigating the eigenvalues and the eigenvectors, we develop conditions on the directed graph for which a stable steady state or a finite eigenvector exists. We demonstrate that each finite eigenvector, characterized as a finite linear combination of a class of eigenvalue, is the minimum among all the feasible schedules and an identical schedule pattern repeats every MPS. We develop an efficient algorithm to find a schedule among such schedules that minimizes a secondary performance measure related to work-in-process inventory. As a by-product of the linear system approach, we also propose a way of characterizing stable steady states of a class of discrete event dynamic systems.

• Korean Journal of Mathematics
• /
• 제8권2호
• /
• pp.155-162
• /
• 2000

For a sequence $\{{\eta}_m\}_m$ of unit vectors in $\mathbb{C}^n$, we consider the associated linear functional ${\omega}$ on the Cuntz algebra $\mathcal{O}_n$. We show that the restriction ${\omega}{\mid}_{UHF_n}$ is the product pure state of a subalgebra $UHF_n$ of $\mathcal{O}_n$ such that ${\omega}{\mid}_{UHF_n}={\otimes}{\omega}_m$ with ${\omega}_m({\cdot})$ < ${\cdot}{\eta}_m,{\eta}_m$ >. We study product pure states of UHF and obtain a concrete description of them in terms of unit vectors. We also study states of $UHF_n$ which is the restriction of the linear functionals on $O_n$ associated to a fixed unit vector in $\mathbb{C}^n$.