Duals of orbit spaces in groups with relatively compact inner automorphism groups are hypergroups |
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Authors: | Dr Klaus Hartmann Dr Rolf Wim Henrichs Dr Rupert Lasser |
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Institution: | (1) Fachbereich 17 (Mathematik/Informatik), Gesamthochschule Paderborn, Warburger Straße 100, D-4790 Paderborn, Federal Republic of Germany;(2) Institut für Mathematik, Technische Universität München, Arcisstraße 21, D-8000 München 2, Federal Republic of Germany |
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Abstract: | For a locally compact groupG and a groupB of topological automorphisms containing the inner automorphisms ofG and being relatively compact with respect to Birkhoff topology (that isG FIA]
B,B
I(G)) the spaceG
B of
-orbits is a commutative hypergroup (=commutative convo inJewett's terminology) in a natural way asJewett has shown. Identifying the space of hypergroup characters ofG
B withE(G, B) (the extreme points ofB-invariant positive definite continuous functionsp withp (e)=1, endowed with the topology of compact convergence) we prove thatE(G, B) is a hypergroup, the hypergroup dual ofG
B. |
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Keywords: | |
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