• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.31-43
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• 1992

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.719-725
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• 2001

For a p-compact group G, if G-space X is of finite S-type then we show that the localization $S^{-1}H^*(X_{hG})$is zero. By using this result, we prove the localization theorem for the pair G-space (X, A)

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.91-95
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• 1988

The nature of a H-set in a Hausdorff space is not well understood. In this note it is shown that if X is a countable union of nowhere dense compact sets, then X is not H-embeddable in any Hausdorff space. An example is given to show that there exists a non-Urysohn, non-H-closed space X such that each H-set of X is compact.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1229-1240
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• 2017

This paper presents a systematic study of the abstract harmonic analysis over spaces of complex measures on homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Then we study abstract harmonic analysis of complex measures over the left coset space G/H.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.441-446
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• 2014

In this paper the following is proved: Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$ and X and Y be operators acting on $\mathcal{H}$. Then there exists a compact operator A in $Alg\mathcal{L}$ such that AX = Y if and only if ${\sup}\{\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}\;:\;f{\in}\mathcal{H},\;E{\in}\mathcal{L}\}$ = K < ${\infty}$ and Y is compact. Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}A{\parallel}=K$.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.9-18
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• 1996

In this paper, we consider the existence of a solution to the elliptic nonlinear partial differential equation ${\Delta}u＋H({\chi})e^{u}$ = 0 (H $\neq$ 0) (1) on a compact manifold without boundary. This equation is related to the problem of a pointwise conformal deformation of metrics on two dimensional compact connected manifolds.(omitted)

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.59-60
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• 1996

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.447-452
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• 2005

Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.755-762
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• 1999

Let X be a p-compace groyp, Y -> X bd a p-compact-subgroup of X and G -> X be a p-compact toral subgroup of X with $(X/Y)^{hG} \neq 0$. In this paper we show that the homotopy fixed point set of the homotopy fibre $(X/Y)^{hG}$ is $F_p$-finite.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.899-910
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• 2012

Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.