Compact Operators for Almost Conservative and Strongly Conservative Matrices

We obtain the necessary and sufficient conditions for an almost conservative matrix to define a compact operator. We also establish some necessary and sufficient (or only sufficient) conditions for operators to be compact for matrix classes (f,X), where X=c,c0,l∞. These results are achieved by apply...

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Main Authors: S. A. Mohiuddine, M. Mursaleen, A. Alotaibi
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/567317
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author S. A. Mohiuddine
M. Mursaleen
A. Alotaibi
author_facet S. A. Mohiuddine
M. Mursaleen
A. Alotaibi
author_sort S. A. Mohiuddine
collection DOAJ
description We obtain the necessary and sufficient conditions for an almost conservative matrix to define a compact operator. We also establish some necessary and sufficient (or only sufficient) conditions for operators to be compact for matrix classes (f,X), where X=c,c0,l∞. These results are achieved by applying the Hausdorff measure of noncompactness.
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institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2014-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-74b45012658b4e7bae17885f5e3e778e2025-02-03T06:06:20ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/567317567317Compact Operators for Almost Conservative and Strongly Conservative MatricesS. A. Mohiuddine0M. Mursaleen1A. Alotaibi2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe obtain the necessary and sufficient conditions for an almost conservative matrix to define a compact operator. We also establish some necessary and sufficient (or only sufficient) conditions for operators to be compact for matrix classes (f,X), where X=c,c0,l∞. These results are achieved by applying the Hausdorff measure of noncompactness.http://dx.doi.org/10.1155/2014/567317
spellingShingle S. A. Mohiuddine
M. Mursaleen
A. Alotaibi
Compact Operators for Almost Conservative and Strongly Conservative Matrices
Abstract and Applied Analysis
title Compact Operators for Almost Conservative and Strongly Conservative Matrices
title_full Compact Operators for Almost Conservative and Strongly Conservative Matrices
title_fullStr Compact Operators for Almost Conservative and Strongly Conservative Matrices
title_full_unstemmed Compact Operators for Almost Conservative and Strongly Conservative Matrices
title_short Compact Operators for Almost Conservative and Strongly Conservative Matrices
title_sort compact operators for almost conservative and strongly conservative matrices
url http://dx.doi.org/10.1155/2014/567317
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AT mmursaleen compactoperatorsforalmostconservativeandstronglyconservativematrices
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