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Yoo, Jong-Kwang;Han, Hyuk
- Journal of the Chungcheong Mathematical Society
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- v.22 no.2
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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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Han, Hyuk
- Communications of the Korean Mathematical Society
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- v.9 no.3
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- pp.617-627
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- 1994
Algebraic spectral subspaces and admissible operators were introduced by K. B. Laursen and M. M. Neumann in 1988 [L88], [N]. These concepts are useful in automatic continuity problems of intertwining linear operators on Banach spaces. In this paper we characterize the algebraic spectral subspaces of generalized scalar operators. From this characterization we show that generalized scalar operators are admissible. Also we show that doubly power bounded operators are generalized scalar. And using the spectral capacity we show that a generalized scalar operator is decomposable. Then we give an example of an operator which is not admissible but decomposable.
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Yoo, Jong-Kwang;Oh, Heung Joon
- Journal of the Chungcheong Mathematical Society
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- v.29 no.4
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- pp.543-552
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- 2016
In this paper we investigate the local spectral properties of quasidecomposable operators. We show that if $T{\in}L(X)$ is quasi-decomposable, then T has the weak-SDP and ${\sigma}_{loc}(T)={\sigma}(T)$. Also, we show that the quasi-decomposability is preserved under commuting quasi-nilpotent perturbations. Moreover, we show that if $f:U{\rightarrow}{\mathbb{C}}$ is an analytic and injective on an open neighborhood U of ${\sigma}(T)$, then $T{\in}L(X)$ is quasi-decomposable if and only if f(T) is quasi-decomposable. Finally, if $T{\in}L(X)$ and $S{\in}L(Y)$ are asymptotically similar, then T is quasi-decomposable if and only if S does.
https://doi.org/10.14403/jcms.2016.29.4.543 인용 PDF KSCI

Park, Sung-Wook;Han, Hyuk;Park, Se Won
- Journal of the Chungcheong Mathematical Society
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- v.16 no.1
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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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