Remarks on orthogonality spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913850652098560 |
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| author | Harding, John Schmeis, Remi Salinas |
| author_facet | Harding, John Schmeis, Remi Salinas |
| contents | We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of $\mathbb{C}^3$ but not of that of $\mathbb{R}^3$. The second is a companion result to the result of Tau and Tserunyan \cite{Tau} that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on orthogonality spaces Harding, John Schmeis, Remi Salinas Mathematical Physics Functional Analysis 06C15, 81P05, 81P10 We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of $\mathbb{C}^3$ but not of that of $\mathbb{R}^3$. The second is a companion result to the result of Tau and Tserunyan \cite{Tau} that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice. |
| title | Remarks on orthogonality spaces |
| topic | Mathematical Physics Functional Analysis 06C15, 81P05, 81P10 |
| url | https://arxiv.org/abs/2505.13871 |