Operator-valued free Fisher information of random matrices
| dc.creator | Meng, Bin | |
| dc.date | 2006-01-22 | |
| dc.date.accessioned | 2026-07-07T06:59:10Z | |
| dc.date.available | 2026-07-07T06:59:10Z | |
| dc.description | We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for $Φ^\ast_{M_2(\mb)}(A,A^\ast,M_2(\mb),η)$, where $A\in M_2(\mb)$ is a $2\times 2$ operator matrix on $\mb$, and $η$ is linear operators on $M_2(\mb)$. Then we consider a special setting: $A$ is an operator-valued semicircular matrix with conditional expectation covariance, and find that $Φ_\mb^\ast(c,c^\ast:\mb,id)=2Index(E)$, where $E$ is a conditional expectation of $\mb$ onto $\md$ and $c$ is a circular variable with covariance $E$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601527 | |
| dc.identifier | http://arxiv.org/abs/math/0601527 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107647 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54, 42C15 | |
| dc.title | Operator-valued free Fisher information of random matrices | |
| dc.type | text |