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

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Ergodic theorems; Spectral theory
Fidaleo, F. (2007). On the entangled ergodic theorem. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 10(1), 67-77 [10.1142/S0219025707002622].
Fidaleo, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/34848
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