• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.715-722
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• 2006

In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.23-29
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• 1985

Let H be an arbitrary complex Hilbert space. We constructed an extension K of H by means of weakly convergent sequences in H and the Banach limit. Let .phi. be the faithful *-representation of L(H) on K. In this note, we investigated the relations between spectra of T in L(H) and .phi.(T) in L(K) and we obtained the following results: 1) If T is a compact operator on H, then .phi.(T) is also a compact operator on K (Proposition 6), 2) .sigma.$_{l}$ (.phi.(T)).contnd..sigma.$_{l}$ (T) for any operator T.mem.L(H) (Corollary 10), 3) For every operator T.mem.L(H), .sigma.$_{ap}$ (.phi.(T))=.sigma.$_{ap}$ (T))=.sigma.$_{ap}$ (T)=.sigma.$_{p}$(.phi.(T)) (Lemma 12, 13) and .sigma.$_{c}$(.phi.(T))=.sigma.(Theorem 15).15).

• Proceedings of the Korea Contents Association Conference
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• 2017.05a
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• pp.431-432
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• 2017

고전 논리의 연산이 집합의 연산과 밀접하게 관련되어 있는 것과 같이 양자논리(quantum logic)는 힐버트 공간(Hilbert space)의 닫힌부분공간(closed subspace)의 연산과 관련되어 있다. 닫힌부분공간들의 집합은 직교모듈로 격자(orthomodular lattice)를 이루고, von Neumann과 Birkhoff를 포함하여 많은 수학자들은 양자논리의 수학적 체계를 만들기 위해 직교모듈로 격자를 이용하였다. 일반 격자(lattice)에서 논리적 함의(implication)는 $x{\rightarrow}y={\neg}x{\vee}y$에 의해 일의적으로 정의되지만 직교모듈로 격자에서는 6개의 서로 다른 논리적 함의가 정의되는 것으로 알려져 있다. 본 논문에서는 직교모듈로 격자에서 정의되는 3개의 논리적 함의를 소개하고 이들 사이의 관계를 조사한다.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.527-535
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies one pair of Torus-Sphere variational linking inequality. We show that I has at least two critical points when I satisfies one pair of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. We prove this result by use of the limit relative category and critical point theory on the manifold with boundary.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.275-283
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• 2015

Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T^∗k(T^∗2T² − 2T^∗T + I)T^k = 0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl’s theorem holds for polynomially k-quasi-2-isometric operators.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.5 no.1
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• pp.38-43
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• 2004

We designed and implemented a medical image query system, including a relational database and DBMS (database management system), which can visualize image data and can achieve spatial, attribute, and mixed queries. Image data used in querying can be visualized in slice, MPR(multi-planner reformat), volume rendering, and overlapping on the query system. To reduce spatial cost and processing time in the system. brain images are spatially clustered, by an adaptive Hilbert curve filling, encoded, and stored to its database without loss for spatial query. Because the query is often applied to small image regions of interest(ROI's), the technique provides higher compression rate and less processing time in the cases.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• East Asian mathematical journal
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• v.26 no.1
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• pp.25-38
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• 2010

In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common mixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.531-540
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• 2015

If T is an unbounded hyponormal operator on an infinite dimensional complex Hilbert space H with ${\rho}(T){\neq}{\phi}$, then it is shown that T satisfies Weyl's theorem, generalized Weyl's theorem, Browder's theorem and generalized Browder's theorem. The equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w) with property (b) have also been established. It is also shown that a-Browder's theorem holds for T as well as its adjoint $T^*$.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.479-487
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• 2009

Let $S(z_1,z_2),\;S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ be power series with operator coefficients such that $S_(z_1,\;z_2)=S_1(z_1,z_2)S_2(z_1,z_2)$. Assume that the multiplications by $S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ are contractive transformations in H($\mathbb{D}^2,\;\mathcal{C}$). Then the factorizations of spaces $\mathcal{D}(\mathbb{D},\;\tilde{S})$ and $\mathcal{D}(\mathbb{D}^2,\mathcal{S})$ are well-behaved.