On absolute, perfect, and unconditional convergences of double series in Banach spaces
We prove that, in the case of double series, perfect and unconditional convergences coincide, while absolute and perfect convergences do not coincide even for numerical series.
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5098 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511298936111104 |
|---|---|
| author | Kadets, M. I. Кадец, M. И. Кадец, M. И. |
| author_facet | Kadets, M. I. Кадец, M. И. Кадец, M. И. |
| author_sort | Kadets, M. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:24:43Z |
| description | We prove that, in the case of double series, perfect and unconditional convergences coincide, while absolute and perfect convergences do not coincide even for numerical series. |
| first_indexed | 2026-03-24T03:10:41Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5098 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:10:41Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b6/4113bf167b17701b07eaa2ee4fbc18b6.pdf |
| spelling | umjimathkievua-article-50982020-03-18T21:24:43Z On absolute, perfect, and unconditional convergences of double series in Banach spaces Об абсолютной, совершенной и безусловной сходимости двойных рядов в пространствах Банаха Kadets, M. I. Кадец, M. И. Кадец, M. И. We prove that, in the case of double series, perfect and unconditional convergences coincide, while absolute and perfect convergences do not coincide even for numerical series. Доведено, що у випадку подвійних рядів досконала та безумовна збіжності співпадають і абсолютна та досконала збіжності не співпадають навіть для числових рядів. Institute of Mathematics, NAS of Ukraine 1997-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5098 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 8 (1997); 1032–1041. August Український математичний журнал; Том 49 № 8 (1997); 1032–1041. August 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5098/6893 https://umj.imath.kiev.ua/index.php/umj/article/view/5098/6894 Copyright (c) 1997 Kadets M. I. |
| spellingShingle | Kadets, M. I. Кадец, M. И. Кадец, M. И. On absolute, perfect, and unconditional convergences of double series in Banach spaces |
| title | On absolute, perfect, and unconditional convergences of double series in Banach spaces |
| title_alt | Об абсолютной, совершенной и безусловной сходимости двойных рядов в пространствах Банаха |
| title_full | On absolute, perfect, and unconditional convergences of double series in Banach spaces |
| title_fullStr | On absolute, perfect, and unconditional convergences of double series in Banach spaces |
| title_full_unstemmed | On absolute, perfect, and unconditional convergences of double series in Banach spaces |
| title_short | On absolute, perfect, and unconditional convergences of double series in Banach spaces |
| title_sort | on absolute, perfect, and unconditional convergences of double series in banach spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5098 |
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