We prove the quantum version of an ergodic result of H. Furstenberg relative to noninvariant measures. The natural setting will be the case of the "quantum diagonal measure" relative to the product measure. Even if in all the interesting situations such diagonal measures are neither invariant nor normal with respect to the corresponding product ones, we still provide an ergodic theorem for them, generalizing the classical case. As a natural application, we are able to prove the entangled ergodic theorem in some interesting situations out of the known ones, that is when the unitary is not almost periodic, or when the involved operators are not compact.

Fidaleo, F. (2009). An ergodic theorem for quantum diagonal measures. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 12(2), 307-320 [10.1142/S0219025709003665].

An ergodic theorem for quantum diagonal measures

FIDALEO, FRANCESCO
2009

Abstract

We prove the quantum version of an ergodic result of H. Furstenberg relative to noninvariant measures. The natural setting will be the case of the "quantum diagonal measure" relative to the product measure. Even if in all the interesting situations such diagonal measures are neither invariant nor normal with respect to the corresponding product ones, we still provide an ergodic theorem for them, generalizing the classical case. As a natural application, we are able to prove the entangled ergodic theorem in some interesting situations out of the known ones, that is when the unitary is not almost periodic, or when the involved operators are not compact.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
eng
Ergodic theorems; Spectral theory
Fidaleo, F. (2009). An ergodic theorem for quantum diagonal measures. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 12(2), 307-320 [10.1142/S0219025709003665].
Fidaleo, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/28752
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