Ergodic Dilation of a Quantum Dynamical System
Confluentes Mathematici, Volume 6 (2014) no. 1, pp. 77-93.

Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.

Received: 2012-08-13
Revised: 2013-11-06
Accepted: 2014-04-18
Published online: 2014-09-09
Classification: 46L07,  46L55,  46L57
Keywords: Quantum Markov process, completely positive maps, Nagy dilation, ergodic state.
     author = {Carlo Pandiscia},
     title = {Ergodic Dilation of a Quantum Dynamical System},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {6},
     number = {1},
     year = {2014},
     pages = {77-93},
     language = {en},
Pandiscia, Carlo. Ergodic Dilation of a Quantum Dynamical System. Confluentes Mathematici, Volume 6 (2014) no. 1, pp. 77-93.

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