We distinguish a class of unbounded operators in , r ≥ 1, related to the self-adjoint operators in 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 -spaces are applied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-5,
author = {Ryszard Jajte},
title = {Pointwise limit theorem for a class of unbounded operators in $^{r}$-spaces},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {49-61},
zbl = {1116.47013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-5}
}
Ryszard Jajte. Pointwise limit theorem for a class of unbounded operators in $^{r}$-spaces. Studia Mathematica, Tome 178 (2007) pp. 49-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-5/