• Title/Summary/Keyword: Fredholm theory

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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.

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.

ON PREHERMITIAN OPERATORS

  • YOO JONG-KWANG;HAN HYUK
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.53-64
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    • 2006
  • In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.