We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the operator A. For the space of James we show that ||I - 2P|| < 2 where P is the canonical projection of the predual of the space. If is a bounded strongly continuous and eventually norm continuous semigroup on a Banach space, we show that if the generator of the semigroup is ergodic, then, for some positive number δ, the operators T(t) - I, 0 < t < δ, are also ergodic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-1-4,
author = {Kirsti Mattila},
title = {On ergodicity for operators with bounded resolvent in Banach spaces},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {63-72},
zbl = {1228.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-1-4}
}
Kirsti Mattila. On ergodicity for operators with bounded resolvent in Banach spaces. Studia Mathematica, Tome 204 (2011) pp. 63-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-1-4/