• 대한수학회보
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• 제35권1호
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• pp.91-97
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• 1998

In this paper we study the Weyl spectrum of weight $\alpha, \omega_\alpha(T)$, of an operator T acting on an infinite dimensional Hilbert space. Main results are as follows. Firstly, we show that the Weyll spectrum of weight $\alpha$ of a polynomially $\alpha$-compact operator is finite, and that similarity preserves polynomial $\alpha$-compactness and the $\alpha$-Weyl's theorem both. Secondly, we give a sufficient condition for an operator to be the sum of an unitary and a $\alpha$-compact operators.

• East Asian mathematical journal
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• 제18권1호
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• pp.21-41
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• 2002

In this paper, we determine the spectrum of the Rhaly matrix $R_a$ as an operator on the space by, when $lim_n(n+1)a_n{\neq}0$ and exists.

• 대한수학회논문집
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• 제18권4호
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• pp.669-676
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• 2003

In 1989, Rhaly [4] determined the spectrum of Rhaly operator $R_{a}$ on the Hilbert space ${\ell}_2$. In this paper Authors determine the spectrum of the Rhaly matrix $R_{a}$ as an operator on the space bvo with assumption $0\;<\;L\;=\;lim_n(n\;+\;1)a_n\;<\;\infty$.

• East Asian mathematical journal
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• 제17권1호
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• pp.87-92
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• 2001

In this paper, we have the extended result of Bunce's theorem. And we show that if T is an irreducible p-hyponormal operator such that T*T-TT* is compact, then ${\sigma}_{ap}(T)={\sigma}_e(T)$ and ${\sigma}_p({\phi}(T))={\sigma}_e({\phi}(T))$.

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.441-455
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• 2017

In this article we have determined the spectrum and fine spectrum of the lower triangular matrix B(r, s) on the Hahn sequence space h. We have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator B(r, s) on the sequence space h.

• 대한수학회지
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• 제33권1호
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• pp.89-99
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• 1996

• 대한수학회보
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• 제60권5호
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• pp.1141-1154
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• 2023

In this paper, we study the complex symmetric weighted composition-differentiation operator D_𝜓,𝜙 with respect to the conjugation JW_𝜉,𝜏 on the Hardy space H². As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of D_𝜓,𝜙 is also investigated.

• 대한수학회지
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• 제54권1호
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• pp.281-302
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• 2017

For a Banach space operator $A{\in}B(\mathcal{X})$, let ${\sigma}(A)$, ${\sigma}_a(A)$, ${\sigma}_w(A)$ and ${\sigma}_{aw}(A)$ denote, respectively, its spectrum, approximate point spectrum, Weyl spectrum and approximate Weyl spectrum. The operator A is polaroid (resp., left polaroid), if the points $iso{\sigma}(A)$ (resp., $iso{\sigma}_a(A)$) are poles (resp., left poles) of the resolvent of A. Perturbation by compact operators preserves neither SVEP, the single-valued extension property, nor the polaroid or left polaroid properties. Given an $A{\in}B(\mathcal{X})$, we prove that a sufficient condition for: (i) A+K to have SVEP on the complement of ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) for every compact operator $K{\in}B(\mathcal{X})$ is that ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) has no holes; (ii) A + K to be polaroid (resp., left polaroid) for every compact operator $K{\in}B(\mathcal{X})$ is that iso${\sigma}_w(A)$ = ∅ (resp., $iso{\sigma}_{aw}(A)$ = ∅). It is seen that these conditions are also necessary in the case in which the Banach space $\mathcal{X}$ is a Hilbert space.

• 대한수학회보
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• 제50권2호
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• pp.499-506
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• 2013

The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if $q(x)$ is prescribed on (0, ${\frac{\pi}{2}}$), then only one spectrum is sufficient to determine $q(x)$ on the interval (0, ${\pi}$) for this problem.

• 대한수학회보
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• 제42권3호
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• pp.543-554
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• 2005

In this paper it is proved that for p-hyponormal or log-hyponormal operator A there exist an associated hyponormal operator T, a quasi-affinity X and an injection operator Y such that TX = XA and AY = YT. The operator A and T have the same spectral picture. We apply these results to give brief proofs of some well known spectral properties of p-hyponormal and log­hyponormal operators, amongst them that the spectrum is a con­tinuous function on these classes of operators.