• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.481-493
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• 2012

Let $S$ be a upper triangular operator such that $M^L_S:\mathcal{U}_2{\rightarrow}\mathcal{U}_2$ defined by $M^L_S(F)=SF$ is a contraction. Then there exists an unitary linear system whose state space is the extension space $\tilde{D}_L$(S) associated with $\mathcal{H}_L$(S).

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.461-468
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• 2004

Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in C(z). The overlapping space $L(\varphi)$ of H(W) in C(z) is a Herglotz space with Herglotz function $\varphi(z)$ which satisfies $\varphi(z)+\varphi^＊(z^{-1})=2[1-W^{*}(z^{-1})W(z)]$. The identity ${}_{L(\varphi)}={-}_{H(W)}$ holds for every f(z) in $L(\varphi)$ and for every vector c.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.301-310
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• 2011

In this paper, we construct the sets of fuzzy matrix pairs. These sets are naturally occurred at the extreme cases for the zero-term rank inequalities derived from the multiplication of fuzzy matrix pairs. We characterize the linear operators that preserve these extreme sets of fuzzy matrix pairs.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.313-321
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• 2023

In this paper, we explore the additivity of the map Ω : 𝒜 → 𝒜 that satisfies Ω([ℒ, ℳ]_*)=[Ω (ℳ), ℒ]_* + [ℳ, Ω(ℒ)]_*, where [ℒ, ℳ]_*= ℒℳ^* - ℳ ℒ^*, for all ℒ, ℳ ∈ 𝒜, a prime *-algebra with unit ℐ. Additionally we show that if Ω (αℐ) is self-adjoint operator for α ∈ {1, i} then Ω = 0.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.773-789
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• 2014

We consider linear operators on square matrices over antinegative semirings. Let ${\varepsilon}_k$ denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set ${\varepsilon}_1$ and the set ${\varepsilon}_2$, and those that preserve the set ${\varepsilon}_{n^2-2n+2}$ and the set ${\varepsilon}_{n^2-2n+1}$. We also characterize those linear operators that strongly preserve ${\varepsilon}_2$, ${\varepsilon}_{n^2-2n+2}$ or ${\varepsilon}_{n^2-2n+1}$.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.133-140
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• 2008

Let {${\xi}_k,\;k\;{\in}\;{\mathbb{Z}}$} be a strictly stationary associated sequence of H-valued random variables with $E{\xi}_k\;=\;0$ and $E{\parallel}{\xi}_k{\parallel}^2\;<\;{\infty}$ and {$a_k,\;k\;{\in}\;{\mathbb{Z}}$} a sequence of linear operators such that ${\sum}_{j=-{\infty}}^{\infty}\;{\parallel}a_j{\parallel}_{L(H)}\;<\;{\infty}$. For a linear process $X_k\;=\;{\sum}_{j=-{\infty}}^{\infty}\;a_j{\xi}_{k-j}$ we derive that {$X_k} fulfills the functional central limit theorem.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.959-965
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• 1996

In this paper we study the index stability theorem for a bounded linear operator with closed range and extend the Kato's decomposition theorem for an absence of the index.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.495-511
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• 2017

In this paper, we consider the system of three elliptic equations using two critical point theorem. We prove the existence of two solutions for suitable forcing terms, under a condition on the linear part which prevents resonance with eigenvalues of the operator.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.775-784
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• 1995

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

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.889-895
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• 1995

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