On a universality property of some abelian Polish groups

Su Gao, and Vladimir Pestov. "On a universality property of some abelian Polish groups." Fundamenta Mathematicae 179.1 (2003): 1-15. <http://eudml.org/doc/282986>.

@article{SuGao2003,
abstract = {We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.},
author = {Su Gao, Vladimir Pestov},
journal = {Fundamenta Mathematicae},
keywords = {Polish group; abelian group; transportation distance; positive definite function; unitary group; group action},
language = {eng},
number = {1},
pages = {1-15},
title = {On a universality property of some abelian Polish groups},
url = {http://eudml.org/doc/282986},
volume = {179},
year = {2003},
}

TY - JOUR
AU - Su Gao
AU - Vladimir Pestov
TI - On a universality property of some abelian Polish groups
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 1
SP - 1
EP - 15
AB - We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
LA - eng
KW - Polish group; abelian group; transportation distance; positive definite function; unitary group; group action
UR - http://eudml.org/doc/282986
ER -