• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.787-792
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• 2010

Let A and B be some standard operator algebras on complex Banach spaces X and Y, respectively. We give the concrete forms of linear idempotence preserving maps $\Phi\;:\;A\;{\rightarrow}\;B$ on finite-rank operators.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.181-190
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• 2013

In this paper we study the Putinar's matricial model operator of rank 2 and provide some evidences for the validity of the conjecture in [8].

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.125-130
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• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.319-331
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• 2019

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.161-170
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• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

• Korean Journal of Computational Design and Engineering
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• v.1 no.3
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• pp.224-233
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• 1996

An automatic mesh generation scheme with triangular finite elements on three-dimensional surfaces has been developed. The surface triangulation process is performed as follows. To begin, surfaces with key nodes are transformed to two-dimensional planes and the meshes with triangular elements are constructed in these planes. Finally, the constructed meshes are transformed back to the original 3D surfaces. For the mesh generation, an irregular mesh generation scheme is employed in which local mesh densities are assigned by the user along the boundaries of the analysis domain. For this purpose a looping algorithm combined with an advancing front technique using basic operators has been developed, in which the loops are recursively subdivided into subloops with the use of the best split lines and then the basic operators generate elements. Using the split lines, the original boundaries are split recursively until each loop contains a certain number of key nodes, and then using the basic operators such as type-1 and type-2, one or two triangular elements are generated at each operation. After the triangulation process has been completed for each meshing domain, the resulting meshes are finally improved by smoothing process. Sample meshes are presented to demonstrate the versatility of the algorithm.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.885-892
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• 2015

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or $T^*$ is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on ${\sigma}(T)$ and is not constant on each connected component of the open set U containing ${\sigma}(T)$. (3) If E is the Riesz idempotent for a nonzero isolated point ${\lambda}$ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

• Communications of the Korean Mathematical Society
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• v.7 no.2
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• pp.307-311
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• 1992

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.261-269
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• 2020

For any Banach spaces X and Y, let L(X, Y) denote the set of all bounded linear operators from X to Y. Let A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA. In this paper, we prove that AC and BA share the local spectral properties such as a finite ascent, a finite descent, property (K), localizable spectrum and invariant subspace.