Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra
We study the relationship between (o)-convergence and almost-everywhere convergence in the Hermite part of the ring of unbounded measurable operators associated with a finite von Neumann algebra. In particular, we prove a theorem according to which (o)-convergence and almost-everywhere convergence a...
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| Дата: | 2003 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2003
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3992 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510123195105280 |
|---|---|
| author | Muratov, M. A. Chilin, V. I. Муратов, M. A Чилин, В. И. Муратов, M. A Чилин, В. И. |
| author_facet | Muratov, M. A. Chilin, V. I. Муратов, M. A Чилин, В. И. Муратов, M. A Чилин, В. И. |
| author_sort | Muratov, M. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:18:03Z |
| description | We study the relationship between (o)-convergence and almost-everywhere convergence in the Hermite part of the ring of unbounded measurable operators associated with a finite von Neumann algebra. In particular, we prove a theorem according to which (o)-convergence and almost-everywhere convergence are equivalent if and only if the von Neumann algebra is of the type I. |
| first_indexed | 2026-03-24T02:51:59Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3992 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:51:59Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/7a/0672e516e290815474ac4cb6f1eb817a.pdf |
| spelling | umjimathkievua-article-39922020-03-18T20:18:03Z Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra Сходимость почти всюду и (o)-сходимосп> в кольцах измеримых операторов, присоединенных к конечной алгебре фон Неймана Muratov, M. A. Chilin, V. I. Муратов, M. A Чилин, В. И. Муратов, M. A Чилин, В. И. We study the relationship between (o)-convergence and almost-everywhere convergence in the Hermite part of the ring of unbounded measurable operators associated with a finite von Neumann algebra. In particular, we prove a theorem according to which (o)-convergence and almost-everywhere convergence are equivalent if and only if the von Neumann algebra is of the type I. Вивчається зв'язок між (o)-збіжністю і збіжністю майже скрізь в ермітовій частині кільця необмежених вимірних операторів, приєднаних до скінченної алгебри фон Неймана. Зокрема, доведено теорему про те, що (o) -збіжність і збіжність майже скрізь еквівалентні тоді і тільки тоді, коли алгебра фон Неймана має тип I. Institute of Mathematics, NAS of Ukraine 2003-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3992 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 9 (2003); 1196-1205 Український математичний журнал; Том 55 № 9 (2003); 1196-1205 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3992/4696 https://umj.imath.kiev.ua/index.php/umj/article/view/3992/4697 Copyright (c) 2003 Muratov M. A.; Chilin V. I. |
| spellingShingle | Muratov, M. A. Chilin, V. I. Муратов, M. A Чилин, В. И. Муратов, M. A Чилин, В. И. Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
| title | Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
| title_alt | Сходимость почти всюду и (o)-сходимосп> в кольцах измеримых операторов, присоединенных к конечной алгебре фон Неймана |
| title_full | Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
| title_fullStr | Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
| title_full_unstemmed | Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
| title_short | Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
| title_sort | almost-everywhere convergence and (o)-convergence in rings of measurable operators associated with a finite von neumann algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3992 |
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