Almost everywhere convergence of
generalized ergodic transforms for
invertible power-bounded operators in $L^p$
Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 61-77
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator $U$ acting on $L^2(X,\varSigma ,\mu )$ ($\mu $ is a $\sigma $-finite measure) may be extended to the case where $U$ is an invertible power-bounded operator acting on $L^p(X,\varSigma ,\mu )$, $p>1$. The proofs make use of the spectral integration initiated by Berkson–Gillespie and, more specifically, of recent results of the author.
Keywords:
results gaposhkin about convergence series associated unitary operator acting varsigma sigma finite measure may extended where invertible power bounded operator acting varsigma proofs make spectral integration initiated berkson gillespie specifically recent results author
Affiliations des auteurs :
Christophe Cuny 1
@article{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 Mathematicum},
pages = {61--77},
year = {2011},
volume = {124},
number = {1},
doi = {10.4064/cm124-1-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-5/}
}
TY - JOUR AU - Christophe Cuny TI - Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^p$ JO - Colloquium Mathematicum PY - 2011 SP - 61 EP - 77 VL - 124 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-5/ DO - 10.4064/cm124-1-5 LA - en ID - 10_4064_cm124_1_5 ER -
%0 Journal Article %A Christophe Cuny %T Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^p$ %J Colloquium Mathematicum %D 2011 %P 61-77 %V 124 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-5/ %R 10.4064/cm124-1-5 %G en %F 10_4064_cm124_1_5
Christophe Cuny. Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^p$. Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 61-77. doi: 10.4064/cm124-1-5
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