Research PapersNo Access

ON THE ENTANGLED ERGODIC THEOREM

FRANCESCO FIDALEO

Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma 00133, Italy

https://doi.org/10.1142/S0219025707002622Cited by:12 (Source: Crossref)

Abstract

Let U be a unitary operator acting on the Hilbert space , and α: {1, …, m} ↦ {1, …, k} a partition of the set {1, …, m}. We show that the ergodic average

converges in the weak operator topology if the A_j belong to the algebra of all the compact operators on

. We write esplicitly 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.

Keywords:

AMSC: 37A30

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