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arXiv · 0706.3620

Hypergroups with Unique Alpha-Means

Ahmadreza Azimifard
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Abstract

Let $K$ be a commutative hypergroup and $α\in \hat{K}$. We show that $K$ is $α$-amenable with the unique $α$-mean $m_α$ if and only if $m_α\in L^1(K)\cap L^2(K)$ and $α$ is isolated in $\hat{K}$. In contrast to the case of amenable noncompact locally compact groups, examples of polynomial hypergroups with unique $α$-means ($α\not=1$) are given. Further examples emphasize that the $α$-amenability of hypergroups depends heavily on the asymptotic behavior of Haar measures and characters.

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Ahmadreza Azimifard. 2008-01-17. Hypergroups with Unique Alpha-Means. https://arxiv.org/abs/0706.3620

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