• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.307-317
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• 2003

For linear operators between Banach algebras "spectral boundedness" is derived from ordinary boundedness by substituting spectral radius for norm. The interplay between this concept and some of its near relatives is conspicuous in a result of Curto and Mathieu.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.35 no.8
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• pp.333-340
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• 1986

This paper presents an approach for determining the discrete reduced-order models for largescale system by using matrix sign function. We define projection operators based on the matrix sign function and develop the algorithm for model-reduction by using them. Simulation studies show that the proposed altgorithm is very useful.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.23-32
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• 1998

In the present paper the author studies the decomposition property ($\delta$) of the bounded linear operators.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.855-861
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• 2007

Let A and B be commuting bounded linear operators on a Hilbert space. In this paper, we study spectral area estimates for norms of $A^*B-BA^*$ when A is subnormal or p-hyponormal.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.1031-1040
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• 2009

It is shown that every almost positive linear mapping h : $\mathcal{A}\rightarrow\mathcal{B}$ of a Banach *-algebra $\mathcal{A}$ to a Banach *-algebra $\mathcal{B}$ is a positive linear operator when h(rx) = rh(x) (r > 1) holds for all $x\in\mathcal{A}$, and that every almost linear mapping h : $\mathcal{A}\rightarrow\mathcal{B}$ of a unital C*-algebra $\mathcal{A}$ to a unital C*-algebra $\mathcal{B}$ is a positive linear operator when h($2^nu*y$) = h($2^nu$)*h(y) holds for all unitaries $u\in \mathcal{A}$, all $y \in \mathcal{A}$, and all n = 0, 1, 2, ..., by using the Hyers-Ulam-Rassias stability of functional equations. Under a more weak condition than the condition as given above, we prove that every almost linear mapping h : $\mathcal{A}\rightarrow\mathcal{B}$ of a unital C*-algebra $\mathcal{A}$ A to a unital C*-algebra $\mathcal{B}$ is a positive linear operator. It is applied to investigate states, center states and center-valued traces.

• Journal of KIISE:Computing Practices and Letters
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• v.5 no.4
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• pp.526-532
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• 1999

본 논문에서는 마이크로프로그램을 위한 테스트 데이타를 자동으로 생성하는 시스템을 제안하였다. 이 시스템에서는 주어진 경로를 따라 마이크로프로그램을 기호수행(symbolic execution)시켜 경로조건식을 구하고 이 식를 풀어서 테스트 데이타를 생성한다. 기호수행 방법을 이용하여 테스트 데이타를 생성하기 위해서는 경로조건식이 선형이어야 한다. 따라서 본 논문에서는 마이크로프로그램의 테스트 데이타를 생성하기 위하여 마이크로프로그램에서 사용되는 연산자들을 선형 연산자로 변환하는 방법을 제안하였다. Abstract In this paper, we propose an automated test data generation system for microprogram. This system symbolically executes microprogram along a given path, extracts path conditions for the given path, and generates test data by solving the path conditions. To generate test data using symbolic execution, the path conditions must be linear. Therefore, we propose a linearization method which transforms operators used in the microprogram into linear operators.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.51-57
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• 2001

Let $\mathcal{B}(H)$ and $\mathcal{B}(K)$ denote the algebras of all bounded linear operators on Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, respectively. We show that if ${\phi}:\mathcal{B}(H){\rightarrow}\mathcal{B}(K)$ is an additive mapping satisfying ${\phi}({\mid}A{\mid}^2)={\mid}{\phi}(A){\mid}^2$ for every $A{\in}\mathcal{B}(H)$, then there exists a mapping ${\psi}$ defined by ${\psi}(A)={\phi}(I){\phi}(A)$, ${\forall}A{\in}\mathcal{B}(H)$ such that ${\psi}$ is the sum of $two^*$-homomorphisms one of which C-linear and the othere C-antilinear. We will also study some conditions implying the injective and rank-preserving of ${\psi}$.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.465-472
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• 2008

For a nonnegative real matrix A of rank 1, A can be factored as $ab^t$ for some vectors a and b. The perimeter of A is the number of nonzero entries in both a and b. If B is a matrix of rank k, then B is the sum of k matrices of rank 1. The perimeter of B is the minimum of the sums of perimeters of k matrices of rank 1, where the minimum is taken over all possible rank-1 decompositions of B. In this paper, we obtain characterizations of the linear operators which preserve perimeters 2 and k for some $k\geq4$. That is, a linear operator T preserves perimeters 2 and $k(\geq4)$ if and only if it has the form T(A) = UAV or T(A) = $UA^tV$ with some invertible matrices U and V.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.5
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• pp.521-528
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• 1999

The nth-order, scalar, linear time-varying (LTV) systems can be dealt with operators on a differential ring. Using this differential algebraic structure and a classical result on differential operator factorizaitons developed by Floquet, a novel eigenstructure(eigenvalues, eigenvectors) concepts for linear time0varying systems are proposed. In this paper, Necessary and sufficient conditions for the existence of well-defined(free of finite-time singularities) SD- and PD- spectra for SPDOs with complex- and real-valued coefficients are also presented. Three numerical examples are presented to illustrate the proposed concepts.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.703-711
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• 2008

Let ${{\xi}_k,k{\in}{\mathbb{Z}}}$ be an associated H-valued random variables with $E{\xi}_k$ = 0, $E{\parallel}{\xi}_k{\parallel}$ < ${\infty}$ and $E{\parallel}{\xi}_k{\parallel}^2$ < ${\infty}$ and {$a_k,k{\in}{\mathbb{Z}}$} a sequence of bounded linear operators such that ${\sum}^{\infty}_{j=0}j{\parallel}a_j{\parallel}_{L(H)}$ < ${\infty}$. We define the sationary Hilbert space process $X_k={\sum}^{\infty}_{j=0}a_j{\xi}_{k-j}$ and prove that $n^{-1}{\sum}^n_{k=1}X_k$ converges to zero.