Determination of the distance from a projection to nilpotents
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917692993175552 |
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| author | Izumi, Masaki Mori, Michiya |
| author_facet | Izumi, Masaki Mori, Michiya |
| contents | In this note, we study the distance from an arbitrary nonzero projection $P$ to the set of nilpotents in a factor $\mathcal{M}$ equipped with a normal faithful tracial state $τ$. We prove that the distance equals $(2\cos \frac{τ(P)π}{1+2τ(P)})^{-1}$. This is new even in the case where $\mathcal{M}$ is the matrix algebra. The special case settles a conjecture posed by Z. Cramer. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_09234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determination of the distance from a projection to nilpotents Izumi, Masaki Mori, Michiya Operator Algebras Functional Analysis In this note, we study the distance from an arbitrary nonzero projection $P$ to the set of nilpotents in a factor $\mathcal{M}$ equipped with a normal faithful tracial state $τ$. We prove that the distance equals $(2\cos \frac{τ(P)π}{1+2τ(P)})^{-1}$. This is new even in the case where $\mathcal{M}$ is the matrix algebra. The special case settles a conjecture posed by Z. Cramer. |
| title | Determination of the distance from a projection to nilpotents |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2406.09234 |