Pairs of Subspaces, Split Quaternions and the Modular Operator
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909529759809536 |
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| author | Naudts, Jan Zhang, Jun |
| author_facet | Naudts, Jan Zhang, Jun |
| contents | We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out, in detail, how two real projection operators lead to the construction of a complex Hilbert space where the theory of the modular operator is applicable, with emphasis on the relevance of a central extension of the group of split quaternions. Two examples are given for which the subspaces have unequal dimension and therefore are not in generic position. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pairs of Subspaces, Split Quaternions and the Modular Operator Naudts, Jan Zhang, Jun Mathematical Physics Functional Analysis 46C05 We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out, in detail, how two real projection operators lead to the construction of a complex Hilbert space where the theory of the modular operator is applicable, with emphasis on the relevance of a central extension of the group of split quaternions. Two examples are given for which the subspaces have unequal dimension and therefore are not in generic position. |
| title | Pairs of Subspaces, Split Quaternions and the Modular Operator |
| topic | Mathematical Physics Functional Analysis 46C05 |
| url | https://arxiv.org/abs/2501.04010 |