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Demicompact linear operators, essential spectrum and some perturbation results
Author(s) -
Chaker Wajdi,
Jeribi Aref,
Krichen Bilel
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200007
Subject(s) - mathematics , essential spectrum , fredholm theory , spectrum (functional analysis) , linear operators , operator theory , bounded operator , bounded function , banach space , operator norm , fredholm operator , pure mathematics , finite rank operator , compact operator , approximation property , resolvent formalism , unbounded operator , fredholm integral equation , mathematical analysis , integral equation , extension (predicate logic) , physics , quantum mechanics , computer science , programming language
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 [27][W. V. Petryshyn, 1972] and Jeribi et al. in [1][B. Abdelmoumen, 2008], [22][K. Latrach, 1996]. 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.