• 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.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.853-869
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• 2018

We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1053-1063
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• 2011

We discuss the perturbation theory of "left" and "right" Browder operators, which come somewhere between Browder operators and semi Browder operators.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.