Reduction of the Gram operator for some classes of the systems of subspaces
UDC 512.552.4 In the investigation of the systems of subspaces with given conditions imposed on the pairs of subspaces, we encounter the problem of nonnegativity of the associated Gram operator.  We prove a theorem that enables us  to reduce the indicated probl...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7915 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512818503090176 |
|---|---|
| author | Strіlets, O. Стрілець, Олександр |
| author_facet | Strіlets, O. Стрілець, Олександр |
| author_sort | Strіlets, O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-27T08:49:56Z |
| description | UDC 512.552.4
In the investigation of the systems of subspaces with given conditions imposed on the pairs of subspaces, we encounter the problem of nonnegativity of the associated Gram operator.  We prove a theorem that enables us  to reduce the indicated problem, for some classes of subspaces, to the problem of nonnegativity of the Gram operator of a ``smaller'' system of subspaces. |
| doi_str_mv | 10.3842/umzh.v76i5.7915 |
| first_indexed | 2026-03-24T03:34:50Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-7915 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:34:50Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/56/4d885cdfd5fd8e13bfb4bb361b771c56 |
| spelling | umjimathkievua-article-79152024-06-27T08:49:56Z Reduction of the Gram operator for some classes of the systems of subspaces Редукція оператора Грама деяких класів систем підпросторів Strіlets, O. Стрілець, Олександр systems of subspaces Gram operator Hilbert space orthogonal projector системи підпросторів оператор Грама гільбертів простір ортогональний проектор UDC 512.552.4 In the investigation of the systems of subspaces with given conditions imposed on the pairs of subspaces, we encounter the problem of nonnegativity of the associated Gram operator.  We prove a theorem that enables us  to reduce the indicated problem, for some classes of subspaces, to the problem of nonnegativity of the Gram operator of a ``smaller'' system of subspaces. УДК 512.552.4 При дослідженні систем підпросторів із заданими умовами для пар підпросторів виникає питання про невід'ємність відповідного оператора Грама. Доведено теорему, яка дозволяє для певного класу систем звести це питання до питання невід'ємності оператора Грама ,,меншої'' системи підпросторів.  Institute of Mathematics, NAS of Ukraine 2024-06-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7915 10.3842/umzh.v76i5.7915 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 5 (2024); 765 - 775 Український математичний журнал; Том 76 № 5 (2024); 765 - 775 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/7915/9946 Copyright (c) 2024 Олександр Стрілець |
| spellingShingle | Strіlets, O. Стрілець, Олександр Reduction of the Gram operator for some classes of the systems of subspaces |
| title | Reduction of the Gram operator for some classes of the systems of subspaces |
| title_alt | Редукція оператора Грама деяких класів систем підпросторів |
| title_full | Reduction of the Gram operator for some classes of the systems of subspaces |
| title_fullStr | Reduction of the Gram operator for some classes of the systems of subspaces |
| title_full_unstemmed | Reduction of the Gram operator for some classes of the systems of subspaces |
| title_short | Reduction of the Gram operator for some classes of the systems of subspaces |
| title_sort | reduction of the gram operator for some classes of the systems of subspaces |
| topic_facet | systems of subspaces Gram operator Hilbert space orthogonal projector системи підпросторів оператор Грама гільбертів простір ортогональний проектор |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7915 |
| work_keys_str_mv | AT stríletso reductionofthegramoperatorforsomeclassesofthesystemsofsubspaces AT strílecʹoleksandr reductionofthegramoperatorforsomeclassesofthesystemsofsubspaces AT stríletso redukcíâoperatoragramadeâkihklasívsistempídprostorív AT strílecʹoleksandr redukcíâoperatoragramadeâkihklasívsistempídprostorív |