Geodesic
Point derivations on the $L^1$-algebra of polynomial hypergroups
Rupert Lasser1
1Institute of Biomathematics and Biometry Helmholtz National Research Center for Environment and Health Ingolstädter Landstraße 1 85764 Neuherberg, Germany and Centre of Mathematics Munich University of Technology 85748 Garching, Germany
Colloquium Mathematicum, Tome 116 (2009) no. 1, pp. 15-30
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We investigate whether the $L^1$-algebra of polynomial hypergroups has non-zero bounded point derivations. We show that the existence of such point derivations heavily depends on growth properties of the Haar weights. Many examples are studied in detail. We can thus demonstrate that the $L^1$-algebras of hypergroups have properties (connected with amenability) that are very different from those of groups.
DOI : 10.4064/cm116-1-2
Keywords: investigate whether algebra polynomial hypergroups has non zero bounded point derivations existence point derivations heavily depends growth properties haar weights many examples studied detail demonstrate algebras hypergroups have properties connected amenability different those groups

Rupert Lasser  1

1 Institute of Biomathematics and Biometry Helmholtz National Research Center for Environment and Health Ingolstädter Landstraße 1 85764 Neuherberg, Germany and Centre of Mathematics Munich University of Technology 85748 Garching, Germany 
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Rupert Lasser. Point derivations on the $L^1$-algebra of
 polynomial hypergroups. Colloquium Mathematicum, Tome 116 (2009) no. 1, pp. 15-30. doi: 10.4064/cm116-1-2

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