On the entangled ergodic theorem

2005/12/13 by Francesco Fidaleo, fidaleo, francesco
Mathematics · #37A30 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0512278

openalex publication_date 2005/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U be a unitary operator acting on the Hilbert space H, and α:\1,..., m\↦\1,..., k\ a partition of the set \1,..., m\. We show that the ergodic average \frac1N^k∑_n₁,...,n_k=0^N-1 U^n_α(1)A₁U^n_α(2)... U^n_α(m-1)A_m-1U^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.

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