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Isomorphisms of hypergroups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Walter R. Bloom  and
Martin E. Walter
Walter R. Bloom
Affiliation:
School of Mathematical and Physical SciencesMurdoch UniversityPerth Western Australia 6150, Australia
Martin E. Walter
Affiliation:
Department of MathematicsUniversity of ColoradoCampus Box 426, Boulder Colorado 80309, USA
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Abstract

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Let K1, K2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L1-algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces.

MSC classification

Secondary: 43A62: Hypergroups 43A10: Measure algebras on groups, semigroups, etc. 43A20: $L^1$-algebras on groups, semigroups, etc. 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 3 , June 1992 , pp. 383 - 400
Copyright
Copyright © Australian Mathematical Society 1992

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