We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.
@article{bwmeta1.element.bwnjournal-article-smv103i1p79bwm,
author = {Mourad Besbes},
title = {Points fixes et th\'eor\`emes ergodiques dans les espaces L$^1$(E)},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {79-97},
zbl = {0810.47049},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i1p79bwm}
}
Besbes, Mourad. Points fixes et théorèmes ergodiques dans les espaces L¹(E). Studia Mathematica, Tome 103 (1992) pp. 79-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i1p79bwm/
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