On characteristic properties of singular operators
For a linear operatorS in a Hilbert space ℋ, the relationship between the following properties is investigated: (i)S is singular (= nowhere closable), (ii) the set kerS is dense in ℋ, and (iii)D(S)∩ℛ(S)={0}.
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| Date: | 1996 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5202 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511409845043200 |
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| author | Koshmanenko, V. D. Ota, S. Кошманенко, В. Д. Ота, Ш. |
| author_facet | Koshmanenko, V. D. Ota, S. Кошманенко, В. Д. Ота, Ш. |
| author_sort | Koshmanenko, V. D. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:27:04Z |
| description | For a linear operatorS in a Hilbert space ℋ, the relationship between the following properties is investigated: (i)S is singular (= nowhere closable), (ii) the set kerS is dense in ℋ, and (iii)D(S)∩ℛ(S)={0}. |
| first_indexed | 2026-03-24T03:12:26Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5202 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:12:26Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/29/478349177a36962ccfaf1e946fce1529.pdf |
| spelling | umjimathkievua-article-52022020-03-18T21:27:04Z On characteristic properties of singular operators Про характеристичні властивості сингулярних операторів Koshmanenko, V. D. Ota, S. Кошманенко, В. Д. Ота, Ш. For a linear operatorS in a Hilbert space ℋ, the relationship between the following properties is investigated: (i)S is singular (= nowhere closable), (ii) the set kerS is dense in ℋ, and (iii)D(S)∩ℛ(S)={0}. Для лінійного оператора $S$ в гільбертовому просторі $ℋ$ досліджується взаємозв'язок між наступними властивостями: 1) $S$ є сингулярним (= ніде не замикальним); 2) множина ker $S$ є щільною в $ℋ$; 3) $D(S) ∩ℛ (S) = \{0\}$. Institute of Mathematics, NAS of Ukraine 1996-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5202 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 11 (1996); 1484-1493 Український математичний журнал; Том 48 № 11 (1996); 1484-1493 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5202/7098 https://umj.imath.kiev.ua/index.php/umj/article/view/5202/7099 Copyright (c) 1996 Koshmanenko V. D.; Ota S. |
| spellingShingle | Koshmanenko, V. D. Ota, S. Кошманенко, В. Д. Ота, Ш. On characteristic properties of singular operators |
| title | On characteristic properties of singular operators |
| title_alt | Про характеристичні властивості сингулярних операторів |
| title_full | On characteristic properties of singular operators |
| title_fullStr | On characteristic properties of singular operators |
| title_full_unstemmed | On characteristic properties of singular operators |
| title_short | On characteristic properties of singular operators |
| title_sort | on characteristic properties of singular operators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5202 |
| work_keys_str_mv | AT koshmanenkovd oncharacteristicpropertiesofsingularoperators AT otas oncharacteristicpropertiesofsingularoperators AT košmanenkovd oncharacteristicpropertiesofsingularoperators AT otaš oncharacteristicpropertiesofsingularoperators AT koshmanenkovd proharakterističnívlastivostísingulârnihoperatorív AT otas proharakterističnívlastivostísingulârnihoperatorív AT košmanenkovd proharakterističnívlastivostísingulârnihoperatorív AT otaš proharakterističnívlastivostísingulârnihoperatorív |