Uniformly cyclic vectors
Colloquium Mathematicum, Tome 104 (2006) no. 1, pp. 21-32
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A group acting on a measure space $(X,\beta,\lambda)$
may or may not
admit a cyclic vector in $L_\infty(X)$. 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.
Keywords:
group acting measure space beta lambda may may admit cyclic vector infty occur acting group group measure preserving transformations does occur even though there cardinality obstruction regular action group itself connection cyclic vectors uniqueness invariant means discussed
Affiliations des auteurs :
Joseph Rosenblatt 1
@article{10_4064_cm104_1_2,
author = {Joseph Rosenblatt},
title = {Uniformly cyclic vectors},
journal = {Colloquium Mathematicum},
pages = {21--32},
publisher = {mathdoc},
volume = {104},
number = {1},
year = {2006},
doi = {10.4064/cm104-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm104-1-2/}
}
Joseph Rosenblatt. Uniformly cyclic vectors. Colloquium Mathematicum, Tome 104 (2006) no. 1, pp. 21-32. doi: 10.4064/cm104-1-2
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