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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| Date: | 2001 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4315 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 \(\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1 - \frac{1}{{n - 1}},n - 1,n} \right\} \supset\) \(\Sigma _n \supset \left\{ {0,1,1 + \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},\left[ {1 + \frac{1}{{n - 3}},n - 1 - \frac{1}{{n - 3}}} \right],n - 1 - \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},n - 1,n} \right\}\) . |
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