• 제목/요약/키워드: analytic spectral subspace

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SPECTRA OF ASYMPTOTICALLY QUASISIMILAR SUBDECOMPOSABLE OPERATORS

  • Yoo, Jong-Kwang;Han, Hyuk
    • 충청수학회지
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    • 제22권2호
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    • pp.271-279
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    • 2009
  • In this paper, we prove that asymptotically quasisimilar sub-decomposable operators have equal spectra and quasisimilar decomposable operators have equal spectra. Moreover, every subscalar operator is admissible.

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LOCAL SPECTRAL PROPERTIES OF SEMI-SHIFTS

  • Yoo, Jong-Kwang;Kim, Yong-Il
    • Journal of applied mathematics & informatics
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    • 제28권1_2호
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    • pp.499-507
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    • 2010
  • In this note, we study the local spectral properties of semi-shifts. If $T\;{\in}\;L(X)$ is a semi-shift on a complex Banach space X, then T is admissible. We also prove that if $T\;{\in}\;L(X)$ is subadmissible, then $X_T(F)\;=\;E_T(F)$ for all closed $F\;{\subseteq}\;\mathbb{C}$. In particular, every subscalar operator on a Banach space is admissible.

ON PREHERMITIAN OPERATORS

  • YOO JONG-KWANG;HAN HYUK
    • 대한수학회논문집
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    • 제21권1호
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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.

ON SPECTRAL SUBSPACES OF SEMI-SHIFTS

  • Han, Hyuk;Yoo, Jong-Kwang
    • 충청수학회지
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    • 제21권2호
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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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SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS

  • Yoo, Jong-Kwang
    • 대한수학회보
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    • 제48권6호
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    • pp.1129-1135
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    • 2011
  • In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

CONTINUITY OF LINEAR OPERATOR INTERTWINING WITH DECOMPOSABLE OPERATORS AND PURE HYPONORMAL OPERATORS

  • Park, Sung-Wook;Han, Hyuk;Park, Se Won
    • 충청수학회지
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    • 제16권1호
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    • pp.37-48
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    • 2003
  • In this paper, we show that for a pure hyponormal operator the analytic spectral subspace and the algebraic spectral subspace are coincide. Using this result, we have the following result: Let T be a decomposable operator on a Banach space X and let S be a pure hyponormal operator on a Hilbert space H. Then every linear operator ${\theta}:X{\rightarrow}H$ with $S{\theta}={\theta}T$ is automatically continuous.

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GENERALIZED INTERTWINING LINEAR OPERATORS WITH ISOMETRIES

  • Hyuk Han
    • 충청수학회지
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    • 제36권1호
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    • pp.13-23
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    • 2023
  • In this paper, we show that for an isometry on a Banach space the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a bounded linear operator with property (δ) on a Banach space X. And let S be an isometry on a Banach space Y . Then every generalized intertwining linear operator θ : X → Y for (S, T) is continuous if and only if the pair (S, T) has no critical eigenvalue.

SOME INVARIANT SUBSPACES FOR BOUNDED LINEAR OPERATORS

  • Yoo, Jong-Kwang
    • 충청수학회지
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    • 제24권1호
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    • pp.19-34
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    • 2011
  • A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.