In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-3,
author = {Delio Mugnolo},
title = {A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {243-251},
zbl = {1067.47011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-3}
}
Delio Mugnolo. A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis. Studia Mathematica, Tome 162 (2004) pp. 243-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-3/