A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in . This can occur when the acting group is as big as the group of all measure-preserving transformations. But it does not occur, even though there is no cardinality obstruction to it, for the regular action of a group on itself. The connection of cyclic vectors to the uniqueness of invariant means is also discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-2,
author = {Joseph Rosenblatt},
title = {Uniformly cyclic vectors},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {21-32},
zbl = {1120.43004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-2}
}
Joseph Rosenblatt. Uniformly cyclic vectors. Colloquium Mathematicae, Tome 106 (2006) pp. 21-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-2/