We show that a stochastic operator acting on the Banach lattice $L^1(m)$ of all $m$-integrable functions on $(X,\,\Cal A)$ is quasi-compact if and only if it is uniformly smoothing (see the definition below).
@article{118745,
author = {Wojciech Bartoszek},
title = {On uniformly smoothing stochastic operators},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {36},
year = {1995},
pages = {203-206},
zbl = {0843.47018},
mrnumber = {1334427},
language = {en},
url = {http://dml.mathdoc.fr/item/118745}
}
Bartoszek, Wojciech. On uniformly smoothing stochastic operators. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 203-206. http://gdmltest.u-ga.fr/item/118745/
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