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be a locally compact group and
a closed subgroup of
be representations of
respectively. Moore’s version of the Frobenius reciprocity theorem was established under the strong conditions that the underlying homogeneous space
possesses a right-invariant measure and the representation space
of the representation
is a Hilbert space. Here, the theorem is proved in a more general setting assuming only the existence of a quasi-invariant measure on
and that the representation spaces
are Banach spaces with
being reflexive. This result was originally established by Kleppner but the version of the proof given here is simpler and more transparent.
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