Demicompact linear operators, essential spectrum and some perturbation results. Issue 13 (15th May 2015)

• Record Type: Journal Article
• Authors: Chaker, Wajdi; Jeribi, Aref; Krichen, Bilel
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 13(2015)
• Page Start: 1476
• Page End: 1486
• Publication Date: 2015-05-15
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201200007
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this paper, we present some results on Fredholm and upper semi‐Fredholm operators involving demicompact operators. Our results generalize many known ones in the literature, in particular those obtained by Petryshyn in <xref ref-type="link" rid="mana201200007-bib-0026">26</xref> and Jeribi et al. in <xref ref-type="link" rid="mana201200007-bib-0001">1</xref>, <xref ref-type="link" rid="mana201200007-bib-0021">21</xref>. They are used to establish a fine description of the Schechter essential spectrum of closed densely defined operators, and to investigate the essential spectrum of the sum of two bounded linear operators defined on a Banach space by means of the essential spectrum of each of the two operators.</p> </abstract>