On the entangled ergodic theorem

dc.creatorfidaleo, francesco
dc.date2005-12-13
dc.date.accessioned2026-07-07T06:55:09Z
dc.date.available2026-07-07T06:55:09Z
dc.descriptionLet $U$ 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.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0512278
dc.identifierhttp://arxiv.org/abs/math/0512278
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106189
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject37A30
dc.titleOn the entangled ergodic theorem
dc.typetext

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