• Title/Summary/Keyword: Fredholm perturbations

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SPECTRA ORIGINATED FROM FREDHOLM THEORY AND BROWDER'S THEOREM

  • Amouch, Mohamed;Karmouni, Mohammed;Tajmouati, Abdelaziz
    • 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.

SOME FREDHOLM THEORY RESULTS AROUND RELATIVE DEMICOMPACTNESS CONCEPT

  • Chaker, Wajdi;Jeribi, Aref;Krichen, Bilel
    • Communications of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.313-325
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    • 2021
  • In this paper, we provide a characterization of upper semi-Fredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.

GENERALIZED BROWDER, WEYL SPECTRA AND THE POLAROID PROPERTY UNDER COMPACT PERTURBATIONS

  • Duggal, Bhaggy P.;Kim, In Hyoun
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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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.