We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator U acting on L²(X,Σ,μ) (μ is a σ-finite measure) may be extended to the case where U is an invertible power-bounded operator acting on , p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-1-5,
author = {Christophe Cuny},
title = {Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^{p}$
},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {61-77},
zbl = {1229.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-1-5}
}
Christophe Cuny. Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^{p}$
. Colloquium Mathematicae, Tome 122 (2011) pp. 61-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-1-5/