On Bi-R-Diagonal Pairs of Operators
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866908894733795328 |
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| author | Katsimpas, Georgios |
| author_facet | Katsimpas, Georgios |
| contents | We study the properties of the analogue of R-diagonal operators in the setting of bi-free probability. Products of bi-R-diagonal pairs of operators that are $*$-bi-free are studied and powers of such pairs are found to also be bi-R-diagonal. It is moreover shown that the joint $*$-distribution of a bi-R-diagonal pair of operators remains invariant under the multiplication by a $*$-bi-free bi-Haar unitary pair and equivalent characterizations of bi-R-diagonal pairs are developed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_01041 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On Bi-R-Diagonal Pairs of Operators Katsimpas, Georgios Operator Algebras 46L54, 46L53 We study the properties of the analogue of R-diagonal operators in the setting of bi-free probability. Products of bi-R-diagonal pairs of operators that are $*$-bi-free are studied and powers of such pairs are found to also be bi-R-diagonal. It is moreover shown that the joint $*$-distribution of a bi-R-diagonal pair of operators remains invariant under the multiplication by a $*$-bi-free bi-Haar unitary pair and equivalent characterizations of bi-R-diagonal pairs are developed. |
| title | On Bi-R-Diagonal Pairs of Operators |
| topic | Operator Algebras 46L54, 46L53 |
| url | https://arxiv.org/abs/1902.01041 |