• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.189-196
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• 2008

In this paper, we study h-stability for linear difference systems by using the notion of $n_{\infty}$-quasisimilarity and discrete Gronwall's inequality.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.91-97
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• 2008

We study h-stability for linear differential systems by using $t_{\infty}$-quasisimilarity and Gronwall's inequality.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.699-710
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• 2021

In this paper, we study various connections of local spectral properties, invariant subspaces, and spectra when an operator S in 𝓛(𝓗) is an ampliation quasiaffine transform of an operator T in 𝓛(𝓗).

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.653-659
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• 2005

In this paper it is proved that quasisimilar n-tuples of tensor products of injective p-quasihyponormal operators have the same spectra, essential spectra and indices, respectively. And it is also proved that a Weyl n-tuple of tensor products of injective p-quasihyponormal operators can be perturbed by an n-tuple of compact operators to an invertible n-tuple.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.11-17
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• 2002

In this paper we give several necessary and sufficient conditions for an operator on the Hilbert space to obey Browder's theorem. And it is shown that if S has totally finite ascent and $T{\prec}S$ then $f(T)$ obeys Browder's theorem for every $f{\in}H({\sigma}(T))$, where $H({\sigma}(T))$ denotes the set of all analytic functions on an open neighborhood of ${\sigma}(T)$.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.287-292
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• 2004

The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.