Quelques résultats sur les opérateurs positifs à moyennes bornées dans \(L_ p\). (French) Zbl 0558.60033
The study of the dominated ergodic theorem for an \(L_ p\) mean bounded positive operator \((p>1)\) is reduced to the study of \(L_ 1\) contractions (resp. \(L_{\infty}\) contractions) with powers converging to zero in \(L_ p\). For every positive \(L_ p\) mean bounded \(L_ 1\) contraction the almost sure convergence theorem is obtained in \(L_ 1\). We show that if T is a non singular \(L_ p(\Omega,{\mathcal A},\mu)\) mean bounded transformation (\(\mu\) finite), then T satisfies the individual ergodic theorem.
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