Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint
This paper is concerned with the relatively bounded perturbations of a closed linear relation and its adjoint in Hilbert spaces. A stability result about orthogonal projections onto the ranges of linear relations is obtained. By using this result, two perturbation theorems for a closed relation and...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/8072295 |
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| _version_ | 1832565422373732352 |
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| author | Guixin Xu |
| author_facet | Guixin Xu |
| author_sort | Guixin Xu |
| collection | DOAJ |
| description | This paper is concerned with the relatively bounded perturbations of a closed linear relation and its adjoint in Hilbert spaces. A stability result about orthogonal projections onto the ranges of linear relations is obtained. By using this result, two perturbation theorems for a closed relation and its adjoint are given. These results generalize the corresponding results for single-valued linear operators to linear relations and some of which weaken certain assumptions of the related existing results. |
| format | Article |
| id | doaj-art-1178dabc2dda490d802626ab36ced2e4 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1178dabc2dda490d802626ab36ced2e42025-02-03T01:07:37ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/8072295Relatively Bounded Perturbations of a Closed Linear Relation and Its AdjointGuixin Xu0School of Mathematics and StatisticsThis paper is concerned with the relatively bounded perturbations of a closed linear relation and its adjoint in Hilbert spaces. A stability result about orthogonal projections onto the ranges of linear relations is obtained. By using this result, two perturbation theorems for a closed relation and its adjoint are given. These results generalize the corresponding results for single-valued linear operators to linear relations and some of which weaken certain assumptions of the related existing results.http://dx.doi.org/10.1155/2022/8072295 |
| spellingShingle | Guixin Xu Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint Discrete Dynamics in Nature and Society |
| title | Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint |
| title_full | Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint |
| title_fullStr | Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint |
| title_full_unstemmed | Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint |
| title_short | Relatively Bounded Perturbations of a Closed Linear Relation and Its Adjoint |
| title_sort | relatively bounded perturbations of a closed linear relation and its adjoint |
| url | http://dx.doi.org/10.1155/2022/8072295 |
| work_keys_str_mv | AT guixinxu relativelyboundedperturbationsofaclosedlinearrelationanditsadjoint |