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

Christophe Cuny

doi:10.4064/cm124-1-5

Geodesic

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

Christophe Cuny ¹

¹ Laboratoire MAS École Centrale de Paris Grande Voie des Vignes 92295 Chatenay-Malabry Cedex, France

Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 61-77.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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.

DOI : 10.4064/cm124-1-5

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

¹ Laboratoire MAS École Centrale de Paris Grande Voie des Vignes 92295 Chatenay-Malabry Cedex, France

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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. http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-5/

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