Stability Theory for Nullity and Deficiency of Linear Relations
Let A and B be two closed linear relations acting between two Banach spaces X and Y, and let λ be a complex number. We study the stability of the nullity and deficiency of A when it is perturbed by λB. In particular, we show the existence of a constant ρ>0 for which both the nullity and deficienc...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/5517215 |
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| _version_ | 1832561492720877568 |
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| author | Silas Luliro Kito Gerald Wanjala |
| author_facet | Silas Luliro Kito Gerald Wanjala |
| author_sort | Silas Luliro Kito |
| collection | DOAJ |
| description | Let A and B be two closed linear relations acting between two Banach spaces X and Y, and let λ be a complex number. We study the stability of the nullity and deficiency of A when it is perturbed by λB. In particular, we show the existence of a constant ρ>0 for which both the nullity and deficiency of A remain stable under perturbation by λB for all λ inside the disk λ<ρ. |
| format | Article |
| id | doaj-art-4888fb7efb93494d8a003358684776ba |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4888fb7efb93494d8a003358684776ba2025-02-03T01:24:54ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/55172155517215Stability Theory for Nullity and Deficiency of Linear RelationsSilas Luliro Kito0Gerald Wanjala1Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, UgandaDepartment of Mathematics, Sultan Qaboos University, P.O. Box 36, PC 123 Al Khoud, OmanLet A and B be two closed linear relations acting between two Banach spaces X and Y, and let λ be a complex number. We study the stability of the nullity and deficiency of A when it is perturbed by λB. In particular, we show the existence of a constant ρ>0 for which both the nullity and deficiency of A remain stable under perturbation by λB for all λ inside the disk λ<ρ.http://dx.doi.org/10.1155/2021/5517215 |
| spellingShingle | Silas Luliro Kito Gerald Wanjala Stability Theory for Nullity and Deficiency of Linear Relations Abstract and Applied Analysis |
| title | Stability Theory for Nullity and Deficiency of Linear Relations |
| title_full | Stability Theory for Nullity and Deficiency of Linear Relations |
| title_fullStr | Stability Theory for Nullity and Deficiency of Linear Relations |
| title_full_unstemmed | Stability Theory for Nullity and Deficiency of Linear Relations |
| title_short | Stability Theory for Nullity and Deficiency of Linear Relations |
| title_sort | stability theory for nullity and deficiency of linear relations |
| url | http://dx.doi.org/10.1155/2021/5517215 |
| work_keys_str_mv | AT silaslulirokito stabilitytheoryfornullityanddeficiencyoflinearrelations AT geraldwanjala stabilitytheoryfornullityanddeficiencyoflinearrelations |