Strongly invariant means on commutative hypergroups

Tom 129 / 2012

Rupert Lasser, Josef Obermaier Colloquium Mathematicum 129 (2012), 119-131 MSC: Primary 43A62; Secondary 43A07. DOI: 10.4064/cm129-1-9

Streszczenie

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.

Autorzy

  • Rupert LasserHelmholtz 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
    e-mail
  • Josef ObermaierHelmholtz National Research Center for Environment and Health
    Institute of Biomathematics and Biometry
    Ingolstädter Landstraße 1
    85764 Neuherberg, Germany
    e-mail

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