Geodesic
Uniformly cyclic vectors
Joseph Rosenblatt1
1 Department of Mathematics University of Illinois at Urbana Urbana, IL 61801, U.S.A.
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.
DOI : 10.4064/cm104-1-2
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

Joseph Rosenblatt 1

1 Department of Mathematics University of Illinois at Urbana Urbana, IL 61801, U.S.A. 
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Joseph Rosenblatt. Uniformly cyclic vectors. Colloquium Mathematicum, Tome 104 (2006) no. 1, pp. 21-32. doi : 10.4064/cm104-1-2. http://geodesic.mathdoc.fr/articles/10.4064/cm104-1-2/

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