JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Strongly invariant means on commutative hypergroups

### Tom 129 / 2012

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

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek