Geodesic
Strongly invariant means on commutative hypergroups
Rupert Lasser1 ; Josef Obermaier2
1 Helmholtz National Research Center for Environment and Health Institute of Biomathematics and Biometry Ingolstädter Landstraße 1 85764 Neuherberg, Germany and Munich University of Technology Centre of Mathematics 85748 Garching, Germany
2 Helmholtz National Research Center for Environment and Health Institute of Biomathematics and Biometry Ingolstädter Landstraße 1 85764 Neuherberg, Germany
Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 119-131

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We introduce and study strongly invariant means $m$ on commutative hypergroups, $m(T_x\varphi \cdot \psi)=m(\varphi \cdot T_{\tilde{x}}\psi)$, $x \in K$, $\varphi,\psi \in L^\infty(K)$. 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.
DOI : 10.4064/cm129-1-9
Keywords: introduce study strongly invariant means commutative hypergroups varphi cdot psi varphi cdot tilde psi varphi psi infty existence means equivalent strong reiter condition polynomial hypergroups derive growth condition haar weights which equivalent existence strongly invariant means apply characterization there commutative hypergroups which possess strongly invariant means

Rupert Lasser 1 ; Josef Obermaier 2

1 Helmholtz National Research Center for Environment and Health Institute of Biomathematics and Biometry Ingolstädter Landstraße 1 85764 Neuherberg, Germany and Munich University of Technology Centre of Mathematics 85748 Garching, Germany
2 Helmholtz National Research Center for Environment and Health Institute of Biomathematics and Biometry Ingolstädter Landstraße 1 85764 Neuherberg, Germany 
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Rupert Lasser; Josef Obermaier. Strongly invariant means on commutative hypergroups. Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 119-131. doi: 10.4064/cm129-1-9

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