Scalar Operators Representable as a Sum of Projectors
We study sets \(\Sigma _n = \{ \alpha \in \mathbb{R}^1 |\) there exist n projectors P1,...,Pn such that \(\sum\nolimits_{k = 1}^n {P_k = \alpha I} \}\) . We prove that if n ≥ 6, then \(\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1...
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| Дата: | 2001 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2001
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4315 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510445505347584 |
|---|---|
| author | Rabanovych, V. I. Samoilenko, Yu. S. Рабанович, В. И. Самойленко, Ю. С. Рабанович, В. И. Самойленко, Ю. С. |
| author_facet | Rabanovych, V. I. Samoilenko, Yu. S. Рабанович, В. И. Самойленко, Ю. С. Рабанович, В. И. Самойленко, Ю. С. |
| author_sort | Rabanovych, V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:26:34Z |
| description | We study sets \(\Sigma _n = \{ \alpha \in \mathbb{R}^1 |\) there exist n projectors P1,...,Pn such that \(\sum\nolimits_{k = 1}^n {P_k = \alpha I} \}\) . We prove that if n ≥ 6, then \(\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1 - \frac{1}{{n - 1}},n - 1,n} \right\} \supset\) \(\Sigma _n \supset \left\{ {0,1,1 + \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},\left[ {1 + \frac{1}{{n - 3}},n - 1 - \frac{1}{{n - 3}}} \right],n - 1 - \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},n - 1,n} \right\}\) . |
| first_indexed | 2026-03-24T02:57:07Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4315 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:57:07Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/53/4f8b71602a24d471b72013493b20fb53.pdf |
| spelling | umjimathkievua-article-43152020-03-18T20:26:34Z Scalar Operators Representable as a Sum of Projectors Скалярные операторы, представимые суммой проекторов Rabanovych, V. I. Samoilenko, Yu. S. Рабанович, В. И. Самойленко, Ю. С. Рабанович, В. И. Самойленко, Ю. С. We study sets \(\Sigma _n = \{ \alpha \in \mathbb{R}^1 |\) there exist n projectors P1,...,Pn such that \(\sum\nolimits_{k = 1}^n {P_k = \alpha I} \}\) . We prove that if n ≥ 6, then \(\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1 - \frac{1}{{n - 1}},n - 1,n} \right\} \supset\) \(\Sigma _n \supset \left\{ {0,1,1 + \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},\left[ {1 + \frac{1}{{n - 3}},n - 1 - \frac{1}{{n - 3}}} \right],n - 1 - \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},n - 1,n} \right\}\) . Вивнаються множини $\Sigma _n = \{ \alpha \in \mathbb{R}^1 |$ існують $n$ проекторів $P_1,...,P_n$ таких, що $\sum\nolimits_{k = 1}^n {P_k = \alpha I} \}$. Доведено: якщо $n ≥ 6$, то $$\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1 - \frac{1}{{n - 1}},n - 1,n} \right\} \supset.$$ Institute of Mathematics, NAS of Ukraine 2001-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4315 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 7 (2001); 939-952 Український математичний журнал; Том 53 № 7 (2001); 939-952 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4315/5334 https://umj.imath.kiev.ua/index.php/umj/article/view/4315/5335 Copyright (c) 2001 Rabanovych V. I.; Samoilenko Yu. S. |
| spellingShingle | Rabanovych, V. I. Samoilenko, Yu. S. Рабанович, В. И. Самойленко, Ю. С. Рабанович, В. И. Самойленко, Ю. С. Scalar Operators Representable as a Sum of Projectors |
| title | Scalar Operators Representable as a Sum of Projectors |
| title_alt | Скалярные операторы, представимые суммой
проекторов |
| title_full | Scalar Operators Representable as a Sum of Projectors |
| title_fullStr | Scalar Operators Representable as a Sum of Projectors |
| title_full_unstemmed | Scalar Operators Representable as a Sum of Projectors |
| title_short | Scalar Operators Representable as a Sum of Projectors |
| title_sort | scalar operators representable as a sum of projectors |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4315 |
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