• Title/Summary/Keyword: Local spectral theory

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On a clary theorem

  • Ko, Eungil
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.29-33
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    • 1996
  • In this paper we shall generalize a Clary theorem by using the local spectral theory; If $ T \in L(H)$ has property $(\beta)$ and A is any operator such that $A \prec T$, then $\sigma(T) \subseteq \sigma(A)$.

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ALGEBRAIC SPECTRAL SUBSPACES OF OPERATORS WITH FINITE ASCENT

  • Han, Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.4
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    • pp.677-686
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    • 2016
  • Algebraic spectral subspaces were introduced by Johnson and Sinclair via a transnite sequence of spaces. Laursen simplified the definition of algebraic spectral subspace. Algebraic spectral subspaces are useful in automatic continuity theory of intertwining linear operators on Banach spaces. In this paper, we characterize algebraic spectral subspaces of operators with finite ascent. From this characterization we show that if T is a generalized scalar operator, then T has finite ascent.

SOME LOCAL SPECTRAL PROPERTIES OF T AND S WITH AT - SA = 0

  • Yoo, Jong-Kwang;Han, Hyuk
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1263-1272
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    • 2008
  • Let T and S be bounded linear operators on Banach spaces X and y, respectively. A linear map A : X ${\rightarrow}$ y is said to be an intertwiner if AT - SA = 0. In this paper we study the relation between local spectral properties of T and S on the assumption of AT - SA = 0. We give some example of intertwiner with T and S.

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ON PREHERMITIAN OPERATORS

  • YOO JONG-KWANG;HAN HYUK
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.53-64
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    • 2006
  • In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.

LOCAL SPECTRAL THEORY AND QUASINILPOTENT OPERATORS

  • YOO, JONG-KWANG
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.785-794
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    • 2022
  • In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then XA(F) = XA+R(F) for all subset F ⊆ ℂ and 𝜎loc(A) = 𝜎loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.

COMMON LOCAL SPECTRAL PROPERTIES OF INTERTWINING LINEAR OPERATORS

  • Yoo, Jong-Kwang;Han, Hyuk
    • Honam Mathematical Journal
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    • v.31 no.2
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    • pp.137-145
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    • 2009
  • Let T ${\in}$ $\mathcal{L}$(X), S ${\in}$ $\mathcal{L}$(Y ), A ${\in}$ $\mathcal{L}$(X, Y ) and B ${\in}$ $\mathcal{L}$(Y,X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares that same local spectral properties SVEP, property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.

LOCAL SPECTRAL THEORY

  • YOO, JONG-KWANG
    • 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.

Earthquake Responses of Nuclear Facilities Subjected to Non-vertically Incidental and Incoherent Seismic Waves (비수직 입사 비상관 지진파에 의한 원전 시설물의 지진 응답)

  • Lee, Jin Ho
    • Journal of the Earthquake Engineering Society of Korea
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    • v.26 no.6
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    • pp.237-246
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    • 2022
  • Based on the random-vibration-theory methodology, dynamic responses of nuclear facilities subjected to obliquely incidental and incoherent earthquake ground motions are calculated. The spectral power density functions of the 6-degree-of-freedom motions of a rigid foundation due to the incoherent ground motions are obtained with the local wave scattering and wave passage effects taken into consideration. The spectral power density function for the pseudo-acceleration of equipment installed on a structural floor is derived. The spectral acceleration of the equipment or the in-structure response spectrum is then estimated using the peak factors of random vibration. The approach is applied to nuclear power plant structures installed on half-spaces, and the reduction of high-frequency earthquake responses due to obliquely incident incoherent earthquake ground motions is examined. The influences of local wave scattering and wave passage effects are investigated for three half-spaces with different shear-wave velocities. When the shear-wave velocity is sufficiently large like hard rock, the local wave scattering significantly affects the reduction of the earthquake responses. In the cases of rock or soft rock, the earthquake responses of structures are further affected by the incident angles of seismic waves or the wave passage effects.

ON SPECTRAL SUBSPACES OF SEMI-SHIFTS

  • Han, Hyuk;Yoo, Jong-Kwang
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.2
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    • pp.247-257
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    • 2008
  • In this paper, we show that for a semi-shift the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a decomposable operator on a Banach space ${\mathcal{X}}$ and let S be a semi-shift on a Banach space ${\mathcal{Y}}$. Then every linear operator ${\theta}:{\mathcal{X}}{\rightarrow}{\mathcal{Y}}$ with $S{\theta}={\theta}T$ is necessarily continuous.

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On the spectral propeties of multipliers

  • Yoo, Jong-Kwang
    • Communications of the Korean Mathematical Society
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    • v.12 no.4
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    • pp.911-920
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    • 1997
  • This note centers around the class M(A) of multipliers on a Gelfand algebra A. This class is a large subalgebra of the Banach algebra L(A). The aim of this note is to investigate some aspects concerning their local spectral properties of multipliers. In the last part of work we consider some applications to automatic continuity theory.

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