Abstract

A hypergroup is a locally compact Hausdorff space equipped with a convolution product which maps any two points to a probability measure with a compact support. Hypergroups generalize locally compact groups in which the above convolution reduces to a point mass measure. It was in the 1970's that Dunkl, Jewett and Spector began the study of hypergroups. Let $K$ be a hypergroup with a Haar measure. In this talk we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant $w^*$-subalgebras of $L_\infty(K)$, and another between compact subhypergroups and a specific subclass of the class of left translation invariant $C^*$-subalgebras of $C_0(K)$. By the help of these two characterizations, we extract some results about invariant complemented subalgebras of $L_\infty(K)$ and $C_0(K)$..



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