Uniformly cyclic vectors

Joseph Rosenblatt. "Uniformly cyclic vectors." Colloquium Mathematicae 104.1 (2006): 21-32. <http://eudml.org/doc/283703>.

@article{JosephRosenblatt2006,
abstract = {A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in $L_\{∞\}(X)$. 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.},
author = {Joseph Rosenblatt},
journal = {Colloquium Mathematicae},
keywords = {cyclic vector; groups of measure-preserving transformations; locally compact groups; amenability; invariant means; uniqueness of invariant means},
language = {eng},
number = {1},
pages = {21-32},
title = {Uniformly cyclic vectors},
url = {http://eudml.org/doc/283703},
volume = {104},
year = {2006},
}

TY - JOUR
AU - Joseph Rosenblatt
TI - Uniformly cyclic vectors
JO - Colloquium Mathematicae
PY - 2006
VL - 104
IS - 1
SP - 21
EP - 32
AB - A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in $L_{∞}(X)$. 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.
LA - eng
KW - cyclic vector; groups of measure-preserving transformations; locally compact groups; amenability; invariant means; uniqueness of invariant means
UR - http://eudml.org/doc/283703
ER -