Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations
The main focus in this paper consists of extending the main results of Diagana (2015) to linear relations. Moreover, we apply our obtained results to study some properties of 3×3-block matrices of linear relations in the form, A≔(ABCDEFGHK). Namely, we show that under some suitable conditions on rel...
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Emerald Publishing
2016-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1319516615000146 |
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doaj-5323e8cc4cdf437fb0d021c7a5c0a1132021-05-02T21:49:47ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662016-01-01221597610.1016/j.ajmsc.2015.05.001Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relationsAymen Ammar0Toka Diagana1Aref Jeribi2Département de Mathématiques, Université de Sfax, Faculté des sciences de Sfax, Route de soukra Km 3.5, B. P. 1171, 3000, Sfax, TunisieDepartment of Mathematics, Howard University, 2441 6th Street N.W., Washington, DC 20059, USADépartement de Mathématiques, Université de Sfax, Faculté des sciences de Sfax, Route de soukra Km 3.5, B. P. 1171, 3000, Sfax, TunisieThe main focus in this paper consists of extending the main results of Diagana (2015) to linear relations. Moreover, we apply our obtained results to study some properties of 3×3-block matrices of linear relations in the form, A≔(ABCDEFGHK). Namely, we show that under some suitable conditions on relations B,C,F,D,G and H, the relation A is closed if and only if A,E and K are closed. In addition, we show that if A,E, K are Fredholm linear relations, then so is the linear relation A.http://www.sciencedirect.com/science/article/pii/S1319516615000146Closed linear relationFredholm linear relation3×3 matrix linear relation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Aymen Ammar Toka Diagana Aref Jeribi |
| spellingShingle |
Aymen Ammar Toka Diagana Aref Jeribi Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations Arab Journal of Mathematical Sciences Closed linear relation Fredholm linear relation 3×3 matrix linear relation |
| author_facet |
Aymen Ammar Toka Diagana Aref Jeribi |
| author_sort |
Aymen Ammar |
| title |
Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations |
| title_short |
Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations |
| title_full |
Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations |
| title_fullStr |
Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations |
| title_full_unstemmed |
Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations |
| title_sort |
perturbations of fredholm linear relations in banach spaces with application to 3×3-block matrices of linear relations |
| publisher |
Emerald Publishing |
| series |
Arab Journal of Mathematical Sciences |
| issn |
1319-5166 |
| publishDate |
2016-01-01 |
| description |
The main focus in this paper consists of extending the main results of Diagana (2015) to linear relations. Moreover, we apply our obtained results to study some properties of 3×3-block matrices of linear relations in the form, A≔(ABCDEFGHK). Namely, we show that under some suitable conditions on relations B,C,F,D,G and H, the relation A is closed if and only if A,E and K are closed. In addition, we show that if A,E, K are Fredholm linear relations, then so is the linear relation A. |
| topic |
Closed linear relation Fredholm linear relation 3×3 matrix linear relation |
| url |
http://www.sciencedirect.com/science/article/pii/S1319516615000146 |
| work_keys_str_mv |
AT aymenammar perturbationsoffredholmlinearrelationsinbanachspaceswithapplicationto33blockmatricesoflinearrelations AT tokadiagana perturbationsoffredholmlinearrelationsinbanachspaceswithapplicationto33blockmatricesoflinearrelations AT arefjeribi perturbationsoffredholmlinearrelationsinbanachspaceswithapplicationto33blockmatricesoflinearrelations |
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1721487079566737408 |