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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: 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

DOI: https://doi.org/10.1090/S0002-9939-1970-0265509-3
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

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