• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.700-705
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• 2012

This paper addresses an intelligent digital redesign (IDR) technique for observer-based output-feedback control systems, in order to efficiently convert a pre-designed Takagi-Sugeno fuzzy model-based analog controller into a sampled-data one in the sense of state matching. A delta operator is used to get an asymptotic relation between the analog and the sampled-data control systems. The IDR problem is viewed as a minimization problem of the norm distances between linear operator to be matched. The condition is represented as linear matrix inequalities, and the separation principle on the IDR is shown.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.553-563
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• 2006

Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ${\sigma}_{B{\omega}}(A)$ of all ${\lambda}{\in}\mathbb{C}$ such that $A-{\lambda}I$ is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem ${\sigma}_{B{\omega}}(A)={\sigma}(A)$\E(A), and the B-Weyl spectrum ${\sigma}_{B{\omega}}(A)$ of A satisfies the spectral mapping theorem. In [51], H. Weyl proved that weyl's theorem holds for hermitian operators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators [12], and to several classes of operators including semi-normal operators ([9], [10]). Recently W. Y. Lee [35] showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee's results to algebraically paranormal operators. In [19] the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in [5], if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above results are generalized by proving that generalizedWeyl's theorem holds for the case where A is an algebraically ($p,\;k$)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1385-1405
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• 2021

Let A be a positive bounded linear operator acting on a complex Hilbert space (𝓗, ⟨·,·⟩). Let ω_A(T) and ║T║_A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (𝓗, ⟨·,·⟩_A), respectively, where ⟨x, y⟩_A := ⟨Ax, y⟩ for all x, y ∈ 𝓗. In this paper, we show with different techniques from that used by Kittaneh in [24] that $$\frac{1}{4}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A{\leq}{\omega}^2_A(T){\leq}\frac{1}{2}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A.$$ Here T^#_A denotes a distinguished A-adjoint operator of T. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the 𝔸-numerical radius of the operator matrix $\(\array{I&T\\0&-I}\)$ where 𝔸 = diag(A, A). In addition, several A-numerical radius inequalities for semi-Hilbert space operators are also established.

• Journal of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-173
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• 1986

• Communications of the Korean Mathematical Society
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• v.8 no.1
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• pp.1-14
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• 1993

• East Asian mathematical journal
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• v.12 no.2
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• pp.167-174
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• 1996

• Journal of the Korean Mathematical Society
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• v.22 no.1
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• pp.35-42
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• 1985

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.277-281
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• 2007

There are many papers on linear operators that preserve commuting pairs of matrices over fields or semirings. From these research works, we have a motivation to the research on the linear operators that preserve commuting pairs of matrices over nonnegative integers. We characterize the surjective linear operators that preserve commuting pairs of matrices over nonnegative integers.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.547-557
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• 2018

We establish some characterizations of isoparametric surfaces in the three-dimensional Euclidean space, which are associated with the Laplacian operator defined by the so-called II-metric on surfaces with non-degenerate second fundamental form and the elliptic linear Weingarten metric on surfaces in the three-dimensional Euclidean space. We also study a Ricci soliton associated with the elliptic linear Weingarten metric.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.