Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

We show the existence of Banach spaces X, Y such that the set of strictly singular operators 𝒮(X,Y) (resp., the set of strictly cosingular operators 𝒞𝒮(X,Y)) would be strictly included in ℱ+(X,Y) (resp., ℱ−(X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ+(X,Y)...

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Main Authors: Abdelkader Dehici, Khaled Saoudi
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2007/26254
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spelling doaj-9a1153e805ef4d43afbbd9b0b0c0a7372020-11-24T23:03:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/2625426254Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm OperatorsAbdelkader Dehici0Khaled Saoudi1Département des Sciences Exactes, Université 8 Mai 1945, Guelma 24000, AlgeriaCentre Universitaire de Khenchela, Route de Batna, El houria, 40004 Khenchela, AlgeriaWe show the existence of Banach spaces X, Y such that the set of strictly singular operators 𝒮(X,Y) (resp., the set of strictly cosingular operators 𝒞𝒮(X,Y)) would be strictly included in ℱ+(X,Y) (resp., ℱ−(X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ+(X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ−(X,Y)).http://dx.doi.org/10.1155/2007/26254
collection DOAJ
language English
format Article
sources DOAJ
author Abdelkader Dehici
Khaled Saoudi
spellingShingle Abdelkader Dehici
Khaled Saoudi
Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
International Journal of Mathematics and Mathematical Sciences
author_facet Abdelkader Dehici
Khaled Saoudi
author_sort Abdelkader Dehici
title Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
title_short Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
title_full Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
title_fullStr Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
title_full_unstemmed Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
title_sort some remarks on perturbation classes of semi-fredholm and fredholm operators
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2007-01-01
description We show the existence of Banach spaces X, Y such that the set of strictly singular operators 𝒮(X,Y) (resp., the set of strictly cosingular operators 𝒞𝒮(X,Y)) would be strictly included in ℱ+(X,Y) (resp., ℱ−(X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ+(X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ−(X,Y)).
url http://dx.doi.org/10.1155/2007/26254
work_keys_str_mv AT abdelkaderdehici someremarksonperturbationclassesofsemifredholmandfredholmoperators
AT khaledsaoudi someremarksonperturbationclassesofsemifredholmandfredholmoperators
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