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A generalisation of the Frobenius Reciprocity theorem
journal contribution
posted on 2023-05-20, 00:59 authored by Hettiarachchilae Dharmadasa, Moran, WLet πΊ be a locally compact group and πΎ a closed subgroup of πΊ. Let πΎ, π be representations of πΎ and πΊ respectively. Mooreβs version of the Frobenius reciprocity theorem was established under the strong conditions that the underlying homogeneous space πΊ/πΎ possesses a right-invariant measure and the representation space π»(πΎ) of the representation πΎ of πΎ is a Hilbert space. Here, the theorem is proved in a more general setting assuming only the existence of a quasi-invariant measure on πΊ/πΎ and that the representation spaces π
(πΎ) and π
(π) are Banach spaces with π
(π) being reflexive. This result was originally established by Kleppner but the version of the proof given here is simpler and more transparent.
History
Publication title
Bulletin of the Australian Mathematical SocietyVolume
100Pagination
317-322ISSN
0004-9727Department/School
School of Natural SciencesPublisher
Australian Mathematics Publ Assoc IncPlace of publication
Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200Rights statement
Copyright 2019 Australian Mathematical Publishing Association Inc.Repository Status
- Restricted