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

Annales de l'institut Fourier (1978)

- Volume: 28, Issue: 2, page 1-23
- ISSN: 0373-0956

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topMathew, 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 -

## References

top- [1] S.C. BAGCHI, J. MATHEW and M.G. NADKARNI, On systems of imprimitivity on locally compact Abelian groups with dense actions, Acta Mathematica (Uppsala), 133 (1974), 287-304. Zbl0325.22003MR54 #7690
- [2] T.W. GAMELIN, Uniform Algebras, Prentice Hall N.J. (U.S.A.), (1969). Zbl0213.40401MR53 #14137
- [3] V.S. VARADARAJAN, Geometry of Quantum Theory, Vol. 2, Van Nostrand Reinhold Co., (1970). Zbl0194.28802MR57 #11400

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