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The structure of hypergroup measure algebras

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

W. Christopher Lang
W. Christopher Lang
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State Mississippi 39762, U.S.A.
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Abstract

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A close analogue for some hypergroup measure algebras of the structure semigroup theorem of J. L. Taylor for convolution measure algebras is constructed: a structure semihypergroup representation is made for the hypergroup measure and its spectrum. This is done for those hypergroup measure algebras that satisfy a condition known as the structure-strong condition. This condition is that the norm-closure of the linear span of the spectrum of the hypergroup measure algebra is a commutative B*-algebra. Then examples of hypergroups whose measure algebras satisfy this condition are given. They include the space of B-orbits of G, where B is a finite solvable group of automorphisms on a locally compact abelian group G. (The hypergroup measure algebra may be identified with the algebra of B-invariant measures on G.) Other examples are the algebra of central measures on a compact, connected, semisimple Lie group, and the algebra of rotation invariant measures on the plane.

Keywords

abstract harmonic analysismeasure algebrashypergroupsstructure semigroups.

MSC classification

Secondary: 43A10: Measure algebras on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 319 - 342
Copyright
Copyright © Australian Mathematical Society 1989

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