Peripheral Poisson Boundary on Full Fock space
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911920145039360 |
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| author | Ghosh, Mainak |
| author_facet | Ghosh, Mainak |
| contents | The operator space generated by peripheral eigenvectors of a unital normal completely positive map $P$ on a von Neumann algebra has a C*-algebra structure. This C*-algebra is known as the \textit{peripheral Poisson boundary} of $P$. For a separable Hilbert space $H$, consider the full fock space defined over $H$. In this paper, we study the peripheral Poisson boundary of the completely positive map, induced by left creation operators of the basis vectors of $H$, on $B(\mcal F(H))$ and explore its behavior with respect to the Poisson boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Peripheral Poisson Boundary on Full Fock space Ghosh, Mainak Operator Algebras Functional Analysis 46L10, 46L54 The operator space generated by peripheral eigenvectors of a unital normal completely positive map $P$ on a von Neumann algebra has a C*-algebra structure. This C*-algebra is known as the \textit{peripheral Poisson boundary} of $P$. For a separable Hilbert space $H$, consider the full fock space defined over $H$. In this paper, we study the peripheral Poisson boundary of the completely positive map, induced by left creation operators of the basis vectors of $H$, on $B(\mcal F(H))$ and explore its behavior with respect to the Poisson boundary. |
| title | Peripheral Poisson Boundary on Full Fock space |
| topic | Operator Algebras Functional Analysis 46L10, 46L54 |
| url | https://arxiv.org/abs/2406.11167 |