Geodesic
Pointwise limit theorem for a class of unbounded operators in $\mathbb L^r$-spaces
Ryszard Jajte 1
1 Faculty of Mathematics University of /L/od/x Banacha 22 90-238 /L/od/x, Poland
Studia Mathematica, Tome 179 (2007) no. 1, pp. 49-61 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We distinguish a class of unbounded operators in ${{\mathbb L}}^r$, $r\geq 1$, related to the self-adjoint operators in ${{\mathbb L}}^2$. For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin's criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in ${{\mathbb L}}^r$-spaces are applied.
DOI : 10.4064/sm179-1-5
Keywords: distinguish class unbounded operators mathbb geq related self adjoint operators mathbb these operators prove kind individual ergodic theorem replacing classical ces averages borel summability result equivalent version gaposhkins criterion convergence operators proof theory martingales interpolation mathbb r spaces applied

Ryszard Jajte  1

1 Faculty of Mathematics University of /L/od/x Banacha 22 90-238 /L/od/x, Poland 
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Ryszard Jajte. Pointwise limit theorem for a class of
 unbounded operators in $\mathbb L^r$-spaces. Studia Mathematica, Tome 179 (2007) no. 1, pp. 49-61. doi: 10.4064/sm179-1-5

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