J Austral Math Soc Ser A 52 pp383--400, 1992.

Isomorphisms of Hypergroups

Walter R. Bloom and Martin E. Walter

Abstract

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.

1991 AMS Subject Classification: primary 43A62; secondary 43A10, 43A20, 43A22

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Authors

Walter R. Bloom

School of Mathematical and Physical Sciences, Murdoch University, Perth, Western Australia 6150, Australia.

Martin E. Walter

Department of Mathematics, University of Colorado, Campus Box 426, Boulder, Colorado 80309, USA.