Strongly invariant means on commutative hypergroups

Rupert Lasser; Josef Obermaier

Colloquium Mathematicae, Tome 126 (2012), p. 119-131 / Harvested from The Polish Digital Mathematics Library

Résumé

We introduce and study strongly invariant means m on commutative hypergroups, $m (T_{x} φ \cdot ψ) = m (φ \cdot T_{x ̃} ψ)$ , x ∈ K, $φ, ψ \in L^{\infty} (K)$ . We show that the existence of such means is equivalent to a strong Reiter condition. For polynomial hypergroups we derive a growth condition for the Haar weights which is equivalent to the existence of strongly invariant means. We apply this characterization to show that there are commutative hypergroups which do not possess strongly invariant means.

Publié le : 2012-01-01

Zbl 1266.43006

EUDML-ID : urn:eudml:doc:283923

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     title = {Strongly invariant means on commutative hypergroups},
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     year = {2012},
     pages = {119-131},
     zbl = {1266.43006},
     language = {en},
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Rupert Lasser; Josef Obermaier. Strongly invariant means on commutative hypergroups. Colloquium Mathematicae, Tome 126 (2012) pp. 119-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-9/