NC functions over the nc Grassmannian
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917223418822656 |
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| author | Ito, Hyuga |
| author_facet | Ito, Hyuga |
| contents | We explain how to formulate Voiculescu's non-commutative Riemann sphere framework for fully matricial functions \cite{v10} within the theory of nc functions developed by Vinnikov and Kaliuzhnyi-Verbovetskyi \cite{kvv14}. We then extend this framework from the Riemann sphere to Grassmannians (and flag manifolds). Moreover, as an example of nc functions in this setting, we introduce a generalization of Voiculescu's non-commutative resolvent on the Riemann sphere, study a corresponding generalization of the resolvent equation, and discuss aspects of the spectral analysis of unbounded operators in Voiculescu's framework \cite{v10}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | NC functions over the nc Grassmannian Ito, Hyuga Functional Analysis Operator Algebras Rings and Algebras We explain how to formulate Voiculescu's non-commutative Riemann sphere framework for fully matricial functions \cite{v10} within the theory of nc functions developed by Vinnikov and Kaliuzhnyi-Verbovetskyi \cite{kvv14}. We then extend this framework from the Riemann sphere to Grassmannians (and flag manifolds). Moreover, as an example of nc functions in this setting, we introduce a generalization of Voiculescu's non-commutative resolvent on the Riemann sphere, study a corresponding generalization of the resolvent equation, and discuss aspects of the spectral analysis of unbounded operators in Voiculescu's framework \cite{v10}. |
| title | NC functions over the nc Grassmannian |
| topic | Functional Analysis Operator Algebras Rings and Algebras |
| url | https://arxiv.org/abs/2601.18041 |