• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1261-1270
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• 2011

In this note we give conditions for continuity of spectrum, approximative point spectrum and defect spectrum on the set $\{T\}+\mathcal{K}(X)$, where $T{\in}\mathcal{B}(X)$ and $\mathcal{K}(X)$ is the set of compact operators.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.487-500
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• 2013

In this paper we provide a brief introduction to the continuity of approximate point spectrum on the algebra B(X), using basic properties of Fredholm operators and the SVEP condition. Also, we give an example showing that in general it not holds that if the spectrum is continuous an operator T, then for each ${\lambda}{\in}{\sigma}_{s-F}(T){\setminus}\overline{{\rho}^{\pm}_{s-F}(T)}$ and ${\in}$ > 0, the ball $B({\lambda},{\in})$ contains a component of ${\sigma}_{s-F}(T)$, contrary to what has been announced in [J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity II, Integral Equations Operator Theory 4 (1981), 459-503] page 462.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.601-605
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• 2015

In the present note, provided $T{\in}{\mathfrak{L}}({\mathfrak{H}})$ is biquasitriangular and Browder's theorem hold for T, we show that the spectrum ${\sigma}$ is continuous at T if and only if the essential spectrum ${\sigma}_e$ is continuous at T.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.65-72
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• 2015

In this paper we show that the spectrum is continuous on the class of ${\star}$-paranormal operators but the approximate point spectrum generally is not continuous at ${\star}$-paranormal operators.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.35-39
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• 2013

Let $(class{\mathcal{A}})^*$ denotes the class of operators satisfying ${\mid}T^2{\mid}{\geq}{\mid}T^*{\mid}^2$. In this paper, we show that the spectrum is continuous on $(class{\mathcal{A}})^*$.

• 한국정보통신설비학회:학술대회논문집
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• 2007.08a
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• pp.354-358
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• 2007

This article presents several methods of mobile communication network to access technologies utilizing unlicensed spectrum interworking. Generic Access Network (GAN) technology was already specified in GERAN (GSM EDGE Radio Access Network) and Interworking WLAN (I-WLAN) was standardized for WCDMA system for WLAN user to access WCDMA packet based services through WLAN access point. Voice Call Continuity is not access network dependent technology but is a kind of domain change scheme for voice call from Circuit Switching (CS) network to IP Multimedia Subsystem (IMS) and vice versa.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.1089-1104
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• 2014

An operator $T{\in}L(H)$, is said to belong to k-quasi class $A_n^*$ operator if $$T^{*k}({\mid}T^{n+1}{\mid}^{\frac{2}{n+1}}-{\mid}T^*{\mid}^2)T^k{\geq}O$$ for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class $A_n^*$. Second, we consider the tensor product for k-quasi class $A_n^*$, giving a necessary and sufficient condition for $T{\otimes}S$ to be a k-quasi class $A_n^*$, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class $A_n^*$ operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and $(B^*)^{-1}$ are k-quasi class $A_n^*$ operators such that AX = XB, then $A^*X=XB^*$. Finally, we will prove the spectrum continuity of this class of operators.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.57-63
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• 2020

We investigate the boundedness of the spectrum of a convex base function for a new function space. The result guarantees the continuity of the Calderón-Zygmund operators on the new space.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.601-614
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• 2018

We consider the magnetic $Schr{\ddot{o}}dinger$ operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.