On the entangled ergodic theorem
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 1, p. 141-156

We study the convergence of the so-called entangled ergodic averages

1Nkn1,...,nk=1NTmnα(m)Am-1Tm-1nα(m-1)Am-2...A1T1nα(1),

where km and α:1,...,m1,...,k is a surjective map. We show that, on general Banach spaces and without any restriction on the partition α, the above averages converge strongly as N under some quite weak compactness assumptions on the operators T j and A j . A formula for the limit based on the spectral analysis of the operators T j and the continuous version of the result are presented as well.

Published online : 2019-02-21
Classification:  47A35,  37A30
@article{ASNSP_2013_5_12_1_141_0,
     author = {Eisner, Tanja and Kunszenti-Kov\'acs, D\'avid},
     title = {On the entangled ergodic theorem},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {1},
     year = {2013},
     pages = {141-156},
     zbl = {1290.47012},
     mrnumber = {3088439},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2013_5_12_1_141_0}
}
Eisner, Tanja; Kunszenti-Kovács, Dávid. On the entangled ergodic theorem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 1, pp. 141-156. http://www.numdam.org/item/ASNSP_2013_5_12_1_141_0/

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