Operator models and analytic subordination for operator-valued free convolution powers
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915782273794048 |
|---|---|
| author | Charlesworth, Ian Jekel, David |
| author_facet | Charlesworth, Ian Jekel, David |
| contents | We revisit the theory of operator-valued free convolution powers given by a completely positive map $η$. We first give a general result, with a new analytic proof, that the $η$-convolution power of the law of $X$ is realized by $V^*XV$ for any operator $V$ satisfying certain conditions, which unifies Nica and Speicher's construction in the scalar-valued setting and Shlyakhtenko's construction in the operator-valued setting. Second, we provide an analog, for the setting of $η$-valued convolution powers, of the analytic subordination for conditional expectations that holds for additive free convolution. Finally, we describe a Hilbert-space manipulation that explains the equivalence between the $n$-fold additive free convolution and the convolution power with respect to $η= n \operatorname{id}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator models and analytic subordination for operator-valued free convolution powers Charlesworth, Ian Jekel, David Operator Algebras 46L54 We revisit the theory of operator-valued free convolution powers given by a completely positive map $η$. We first give a general result, with a new analytic proof, that the $η$-convolution power of the law of $X$ is realized by $V^*XV$ for any operator $V$ satisfying certain conditions, which unifies Nica and Speicher's construction in the scalar-valued setting and Shlyakhtenko's construction in the operator-valued setting. Second, we provide an analog, for the setting of $η$-valued convolution powers, of the analytic subordination for conditional expectations that holds for additive free convolution. Finally, we describe a Hilbert-space manipulation that explains the equivalence between the $n$-fold additive free convolution and the convolution power with respect to $η= n \operatorname{id}$. |
| title | Operator models and analytic subordination for operator-valued free convolution powers |
| topic | Operator Algebras 46L54 |
| url | https://arxiv.org/abs/2501.09690 |