The entangled ergodic theorem in the almost periodic case

Details The entangled ergodic theorem in the almost periodic case The entangled ergodic theorem in the almost periodic case

2009-08-30

arxiv.org/abs/0908.4395v1

Mathematics

Functional Analysis

13 pages, accepted for publication in Linear Algebra and its Applications

Scientific paper

Let $U$ be a unitary operator acting on the Hilbert space $\ch$, and $\a:\{1,..., 2k\}\mapsto\{1,..., k\}$ a pair partition. Then the ergodic average $$ \frac{1}{N^{k}}\sum_{n_{1},...,n_{k}=0}^{N-1} U^{n_{\a(1)}}A_{1}U^{n_{\a(2)}}... U^{n_{\a(2k-1)}}A_{2k-1}U^{n_{\a(2k)}} $$ converges in the strong operator topology provided $U$ is almost periodic, that is when $\ch$ is generated by the eigenvalues of $U$. We apply the present result to obtain the convergence of the Cesaro mean of several multiple correlations.

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