On systems of imprimitivity on locally compact abelian groups with dense actions

Mathew, J., and Nadkarni, M. G.. "On systems of imprimitivity on locally compact abelian groups with dense actions." Annales de l'institut Fourier 28.2 (1978): 1-23. <http://eudml.org/doc/74356>.

@article{Mathew1978,
abstract = {Consider the four pairs of groups $(\Gamma ,R)$, $(\Gamma /\Gamma _0,R/\Gamma _0)$, $(K\cap S,P)$ and $(S,B)$, where $\Gamma $, $R$ are locally compact second countable abelian groups, $\Gamma $ is a dense subgroup of $R$ with inclusion map from $\Gamma $ to $R$ continuous; $\Gamma _0\subseteq \Gamma \subseteq R$ is a closed subgroup of $R$; $S$, $B$ are the duals of $R$ and $\Gamma $ respectively, and $K$ is the annihilator of $\Gamma _0$ in $B$. Let the first co-ordinate of each pair act on the second by translation. We connect, by a commutative diagram, the systems of imprimitivity which arise in a natural fashion on each pair, starting with a system of imprimitivity on one of the pairs (see section 1 for details).},
author = {Mathew, J., Nadkarni, M. G.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {1-23},
publisher = {Association des Annales de l'Institut Fourier},
title = {On systems of imprimitivity on locally compact abelian groups with dense actions},
url = {http://eudml.org/doc/74356},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Mathew, J.
AU - Nadkarni, M. G.
TI - On systems of imprimitivity on locally compact abelian groups with dense actions
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 1
EP - 23
AB - Consider the four pairs of groups $(\Gamma ,R)$, $(\Gamma /\Gamma _0,R/\Gamma _0)$, $(K\cap S,P)$ and $(S,B)$, where $\Gamma $, $R$ are locally compact second countable abelian groups, $\Gamma $ is a dense subgroup of $R$ with inclusion map from $\Gamma $ to $R$ continuous; $\Gamma _0\subseteq \Gamma \subseteq R$ is a closed subgroup of $R$; $S$, $B$ are the duals of $R$ and $\Gamma $ respectively, and $K$ is the annihilator of $\Gamma _0$ in $B$. Let the first co-ordinate of each pair act on the second by translation. We connect, by a commutative diagram, the systems of imprimitivity which arise in a natural fashion on each pair, starting with a system of imprimitivity on one of the pairs (see section 1 for details).
LA - eng
UR - http://eudml.org/doc/74356
ER -