An imprimitivity theorem for hypergroups (Q1099362)

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scientific article; zbMATH DE number 4040529
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An imprimitivity theorem for hypergroups
scientific article; zbMATH DE number 4040529

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    An imprimitivity theorem for hypergroups (English)
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    1988
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    Let K be a hypergroup, H a closed subgroup of K such that K/H is paracompact and U a representation of K in a Hilbert space E. Let \(P: C_ 0(K/H)\to B(E)\) be an essental *-representation of the algebra \(C_ 0(K/H)\) such that \(U(a)P(g)=P(_ ag)U(a)\) for all \(a\in K\) and \(g\in C_ 0(K/H)\). The author establishes the existence of a unitary mapping \(W: E\to F\) such that \(WU(a)=U(a)W\) and \(WP(g)=P(g)W\) for all \(a\in K\) and \(g\in C_ 0(K/H)\).
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    hypergroup
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    Hilbert space
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    essental *-representation
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    unitary mapping
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