• 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 X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.535-543
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• 2009

In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford's boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford's boundedness condition (B).

• Bulletin of the Korean Mathematical Society
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• v.18 no.1
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• pp.15-16
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• 1981

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.489-499
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• 1998

Let A be the non-commutative Banach algebra with identity satisfying certain conditions. We show that if D is a derivation on A, then D(A) is contained in the radical of A.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.257-262
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• 2014

In this note we consider "generalized Riesz points" for compact and quasinilpotent perturbations of Toeplitz operators acting on the Hardy space of the unit circle.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.611-630
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• 1999

In this paper we show that the Derivation D(A) on the non-commutative Banach algebra A with identity satisfying certain conditions is contained in the radical of A and will show some examples satisfying such properties.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.869-873
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• 2005

In this note we give a positive answer to the conjecture by Fong and Istratescu.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.203-209
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• 2009

In this paper we study some spectral properties of the class (y) operators and we will investigate on the relation between this class and other usual classes of operators.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.273-286
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• 2023

In this paper we show that if T ∈ L(X) and S ∈ L(X) is a Riesz operator commuting with T and X_S(F) ∈ Lat(S), where F = {0} or F ⊆ ℂ ⧵ {0} is closed then T|X_S(F) and T|X_T(F) + S|X_S(F) share the local spectral properties such as SVEP, Dunford's property (C), Bishop's property (𝛽), decomopsition property (𝛿) and decomposability. As a corollary, if T ∈ L(X) and Q ∈ L(X) is a quasinilpotent operator commuting with T then T is Riesz if and only if T + Q is Riesz. We also study some spectral properties of Riesz operators acting on Banach spaces. We show that if T, S ∈ L(X) such that TS = ST, and Y ∈ Lat(S) is a hyperinvarinat subspace of X for which 𝜎(S|Y ) = {0} then 𝜎_*(T|Y + S|Y ) = 𝜎_*(T|Y ) for 𝜎_* ∈ {𝜎, 𝜎_loc, 𝜎_sur, 𝜎_ap}. Finally, we show that if T ∈ L(X) and S ∈ L(Y ) on the Banach spaces X and Y and T is similar to S then T is Riesz if and only if S is Riesz.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.671-677
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• 2006

Let $A, B{\in}B(H)$ be Hilbert space contractions, and let ${\Delta}_{AB}$ be the elementary operator ${\Delta}_{AB}:X{\rightarrow}AXB-X$. A number of conditions which are equivalent to '${\Delta}_{AB}$ has closed range' are proved.