Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^p$

Christophe Cuny. "Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^{p}$." Colloquium Mathematicae 124.1 (2011): 61-77. <http://eudml.org/doc/283469>.

@article{ChristopheCuny2011,
abstract = {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 $L^\{p\}(X,Σ,μ)$, p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.},
author = {Christophe Cuny},
journal = {Colloquium Mathematicae},
keywords = {Berkson-Gillespie spectral integral; spaces; ergodic transforms; almost everywhere convergence},
language = {eng},
number = {1},
pages = {61-77},
title = {Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^\{p\}$},
url = {http://eudml.org/doc/283469},
volume = {124},
year = {2011},
}

TY - JOUR
AU - Christophe Cuny
TI - Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^{p}$
JO - Colloquium Mathematicae
PY - 2011
VL - 124
IS - 1
SP - 61
EP - 77
AB - 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 $L^{p}(X,Σ,μ)$, p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.
LA - eng
KW - Berkson-Gillespie spectral integral; spaces; ergodic transforms; almost everywhere convergence
UR - http://eudml.org/doc/283469
ER -