Let U be a unitary operator acting on the Hilbert space H, and alpha : {1....,m} -> {1,...,k} a partition of the set {1,...,m}. We show that the ergodic average [GRAPHICS] U-n alpha (1) A(1)U(n alpha (2))... Un alpha (m-1) A(m-1)U(n alpha (m)) converges in the weak operator topology if the A(j) belong to the algebra of all the compact operators on H. 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.
Fidaleo, F. (2007). On the entangled ergodic theorem. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 10(1), 67-77 [10.1142/S0219025707002622].
On the entangled ergodic theorem
FIDALEO, FRANCESCO
2007-01-01
Abstract
Let U be a unitary operator acting on the Hilbert space H, and alpha : {1....,m} -> {1,...,k} a partition of the set {1,...,m}. We show that the ergodic average [GRAPHICS] U-n alpha (1) A(1)U(n alpha (2))... Un alpha (m-1) A(m-1)U(n alpha (m)) converges in the weak operator topology if the A(j) belong to the algebra of all the compact operators on H. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
