On the entangled ergodic theorem
| dc.creator | fidaleo, francesco | |
| dc.date | 2005-12-13 | |
| dc.date.accessioned | 2026-07-07T06:55:09Z | |
| dc.date.available | 2026-07-07T06:55:09Z | |
| dc.description | Let $U$ be a unitary operator acting on the Hilbert space H, and $α:\{1,..., m\}\mapsto\{1,..., k\}$ a partition of the set $\{1,..., m\}$. We show that the ergodic average $$ \frac{1}{N^{k}}\sum_{n_{1},...,n_{k}=0}^{N-1} U^{n_{α(1)}}A_{1}U^{n_{α(2)}}... U^{n_{α(m-1)}}A_{m-1}U^{n_{α(m)}} $$ converges in the weak operator topology if the $A_{j}$ belong to the algebra of all the compact operators on H. We write esplicitely the formula for these ergodic averages in the case of pair--partitions. Some results without any restriction on the operators $A_{j}$ are also presented in the almost periodic case. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512278 | |
| dc.identifier | http://arxiv.org/abs/math/0512278 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106189 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 37A30 | |
| dc.title | On the entangled ergodic theorem | |
| dc.type | text |