ON THE ENTANGLED ERGODIC THEOREM

Abstract

Let U be a unitary operator acting on the Hilbert space [Formula: see text], and α: {1, …, m} ↦ {1, …, k} a partition of the set {1, …, m}. We show that the ergodic average [Formula: see text] converges in the weak operator topology if the A j belong to the algebra of all the compact operators on [Formula: see text]. 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.

Locations

• Infinite Dimensional Analysis Quantum Probability and Related Topics - View
• arXiv (Cornell University) - View - PDF