The entangled ergodic theorem in the almost periodic case

2009/08/30 by Francesco Fidaleo, Fidaleo, Francesco · 1 citation
Mathematics · #37A30 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0908.4395

openalex publication_date 2009/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U be a unitary operator acting on the Hilbert space \ch, and \a:\1,..., 2k\↦\1,..., k\ a pair partition. Then the ergodic average \frac1N^k∑_n₁,...,n_k=0^N-1 U^n_\a(1)A₁U^n_\a(2)... U^n_\a(2k-1)A_2k-1U^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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• Ergodic Theory of Inhomogeneous Quantum Processes

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