Operator Projective Line and Its Transformations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914889252995072 |
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| author | Aljasem, Jafar Kisil, Vladimir V. |
| author_facet | Aljasem, Jafar Kisil, Vladimir V. |
| contents | We introduce a concept of the operator (non-commutative) projective line PH defined by a Hilbert space H and a symplectic structure on it. Points of PH are Lagrangian subspaces of H. If a particular Lagrangian subspace is fixed then we can define SL(2,R)-action on PH. This gives a consistent framework for linear fractional transformations of operators. Some connections with spectral theory are outline as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator Projective Line and Its Transformations Aljasem, Jafar Kisil, Vladimir V. Functional Analysis Mathematical Physics Spectral Theory 46C05, 47A11, 53D05, 81S10 We introduce a concept of the operator (non-commutative) projective line PH defined by a Hilbert space H and a symplectic structure on it. Points of PH are Lagrangian subspaces of H. If a particular Lagrangian subspace is fixed then we can define SL(2,R)-action on PH. This gives a consistent framework for linear fractional transformations of operators. Some connections with spectral theory are outline as well. |
| title | Operator Projective Line and Its Transformations |
| topic | Functional Analysis Mathematical Physics Spectral Theory 46C05, 47A11, 53D05, 81S10 |
| url | https://arxiv.org/abs/2402.02595 |