Relative Positions of Half-sided Modular Inclusions
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915211259150336 |
|---|---|
| author | Koot, Ian |
| author_facet | Koot, Ian |
| contents | Let $K_1 \subset H$ and $K_2 \subset H$ be half-sided modular inclusions in a common standard subspace $H$. We prove that the inclusion $K_1 \subset K_2$ holds if and only if we have an inclusion of spectral subspaces of the generators of the positive one-parameter groups associated to the half-sided modular inclusions $K_1 \subset H$ and $K_2 \subset H$. From this we give a characterization of this situation in terms of (operator valued) symmetric inner functions. We illustrate these characterizations with some examples of non-trivial phenomena occurring in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative Positions of Half-sided Modular Inclusions Koot, Ian Mathematical Physics Operator Algebras Let $K_1 \subset H$ and $K_2 \subset H$ be half-sided modular inclusions in a common standard subspace $H$. We prove that the inclusion $K_1 \subset K_2$ holds if and only if we have an inclusion of spectral subspaces of the generators of the positive one-parameter groups associated to the half-sided modular inclusions $K_1 \subset H$ and $K_2 \subset H$. From this we give a characterization of this situation in terms of (operator valued) symmetric inner functions. We illustrate these characterizations with some examples of non-trivial phenomena occurring in this setting. |
| title | Relative Positions of Half-sided Modular Inclusions |
| topic | Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2503.18036 |