Strongly invariant means on commutative hypergroups

• Autorzy: Rupert Lasser , Josef Obermaier
• Języki publikacji: EN

Abstrakty

EN

We introduce and study strongly invariant means m on commutative hypergroups, $m(T_{x}φ · ψ) = m(φ · T_{x̃}ψ)$, x ∈ K, $φ,ψ ∈ L^{∞}(K)$. 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.

Kategorie tematyczne

• 43A62: Hypergroups
• 43A07: Means on groups, semigroups, etc.; amenable groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 1
• Strony: 119-131

Daty

wydano

2012

Twórcy

autor

Rupert Lasser

• Helmholtz National Research Center, for Environment and Health, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany
• Munich University of Technology, Centre of Mathematics, 85748 Garching, Germany

autor

Josef Obermaier

• Helmholtz National Research Center for Environment and Health, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany

Identyfikatory

DOI

10.4064/cm129-1-9