Isometric Operators on L1-Algebras of Hypergroups

Nobuaki Obata
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Nobuaki Obata: Universität Tübingen, Mathematisches Institut

A chapter in Probability Measures on Groups X, 1991, pp 315-328 from Springer

Abstract: Abstract In recent years hypergroups, in particular commutative ones have been considerably discussed keeping a profound contact with harmonic analysis and probability theory2. The study of hypergroup-isomorphisms, however, has remained an interesting area that needs investigating, though the basic concepts were already introduced by Jewett [7] in 1975. A noteworthy approach to this subject has been initiated by Bloom and Walter [2] only recently. They have studied an analogue of Wendel’s theorem for hypergroups, namely, established a relationship between hypergroup-isomorphisms and isometric isomorphisms among L 1 -algebras. Motivated by their work, we study in this paper the maximum subgroup of a hypergroup in terms of isometric operators acting on L 1-algebras. As a result, we obtain a characterization of locally compact groups among hypergroups. Our discussion being based on L 1 -algebras of hypergroups, we always assume that every hypergroup under discussion admits a left invariant measure.

Keywords: Compact Group; Maximum Subgroup; Point Mass; Weak Topology; Approximate Identity (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2364-6_24

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DOI: 10.1007/978-1-4899-2364-6_24

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