• Honam Mathematical Journal
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• v.42 no.4
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• pp.821-828
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• 2020

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.423-430
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• 2002

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{}i$ = $Y_{i}$ for i/ = 1,2,…, n. In this article, we obtained the following : Let X ＝ ($x_{i\sigma(i)}$ and Y ＝ ($y_{ij}$ be operators in B(H) such that $X_{i\sigma(i)}\neq\;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${\frac{\parallel{\sum^n}_{i=1}E_iYf_i\parallel}{\parallel{\sum^n}_{i=1}E_iXf_i\parallel}n\;\epsilon\;N,E_i\;\epsilon\;L and f_i\;\epsilon\;H}$ < $\infty$ and $x_{i,\sigma(i)}y_{i,\sigma(i)}$ is real for all i = 1,2, ....

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.215-223
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• 2017

In this paper, we establish results about operators similar to their adjoints. This is carried out in the setting of bounded and also unbounded operators on a Hilbert space. Among the results, we prove that an unbounded closed operator similar to its adjoint, via a cramped unitary operator, is self-adjoint. The proof of this result works also as a new proof of the celebrated result by Berberian on the same problem in the bounded case. Other results on similarity of hyponormal unbounded operators and their self-adjointness are also given, generalizing well known results by Sheth and Williams.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.55-60
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• 2007

Given operators X and Y acting on a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we showed the following : Let $\cal{L}$ be a subspace lattice acting on a Hilbert space $\cal{H}$ and let X and Y be operators in $\cal{B}(\cal{H})$. Let P be the projection onto $\bar{rangeX}$. If FE = EF for every $E\in\cal{L}$, then the following are equivalent: (1) $sup\{{{\parallel}E^{\perp}Yf\parallel\atop \parallel{E}^{\perp}Xf\parallel}\;:\;f{\in}\cal{H},\;E\in\cal{L}\}\$ < $\infty$, $\bar{range\;Y}\subset\bar{range\;X}$, and < Xf, Yg >=< Yf,Xg > for any f and g in $\cal{H}$. (2) There exists a self-adjoint operator A in Alg$\cal{L}$ such that AX = Y.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.237-249
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• 2004

Consider the second order self-adjoint neutral difference equation of form $\Delta(a_n$\mid$\Delta(x_n\;-\;{p_n}{x_{{\tau}_n}}$\mid$^{\alpha}sgn{\Delta}(x_n\;-\;{p_n}{x_{{\tau}_n}}\;+\;f(n,\;{x_{g_n}}\;=\;0$. In this paper, we will give the classification of nonoscillatory solutions of the above equation; and by the fixed point theorem, we present some existence results for some kinds of nonoscillatory solutions of the equation.

• Journal of KSNVE
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• v.4 no.1
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• pp.51-57
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• 1994

The objective of this research is to introduce a method of modal identification for self-adjoint distributed parameter systems using Spatial Fiter. To minimize the spillover effects which come from using the finite discrete sensors by means of discrete measurements, a new mechanism, namely spatial filter which is main subject in this research, is introduced for extracting modal coordinates from sensors' output. As an illustration of the proposed method, two simple numerical examples are also examined.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.679-686
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• 2017

The present paper is devoted to self-adjoint cyclically compact operators on Hilbert-Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators is given. We use more simple and constructive method, which allowed to apply this result to compact operators relative to von Neumann algebras. Namely, a general form of compact operators relative to a type I von Neumann algebra is given.

• Proceedings of the Korean Nuclear Society Conference
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• 2003.10a
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• pp.53.2-53.2
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• 2003

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.701-716
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• 2021

In this present article, we construct a new framework that's we call the weighted geometric realization of 2 and 3-simplexes. On this new weighted framework, we construct a nonself-adjoint 2-simplex Laplacian L and a self-adjoint 2-simplex Laplacian N. We propose general conditions to ensure sectoriality for our new nonself-adjoint 2-simplex Laplacian L. We show the relation between the essential spectra of L and N. Finally, we prove the absence of the essential spectrum for our 2-simplex Laplacians L and N.

• Kyungpook Mathematical Journal
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• v.21 no.1
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• pp.9-14
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• 1981