Dimensionality and the duals of certain locally compact groups
Author:
I. Schochetman
Journal:
Proc. Amer. Math. Soc. 26 (1970), 514-520
MSC:
Primary 22.20
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265509-3
MathSciNet review:
0265509
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Abstract | References | Similar Articles | Additional Information
Abstract: Let $G$ be a separable locally compact group containing a closed normal subgroup which is type I and regularly embedded. The elements of the dual space $G$ are known to be induced from certain closed subgroups. In this article we first determine the kernel of an induced representation and then give necessary and sufficient conditions for $G$ to be maximally almost periodic. These results are then applied to the collection of compact extensions of abelian groups.
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Additional Information
Keywords:
Locally compact group,
normal subgroup,
group extension,
dual space,
finite dimensional representation,
irreducible representation,
kernel of a representation,
induced representation,
maximally almost periodic
Article copyright:
© Copyright 1970
American Mathematical Society