Point derivations on the $L^1$-algebra of polynomial hypergroups

Volume 116 / 2009

Rupert Lasser Colloquium Mathematicum 116 (2009), 15-30 MSC: 43A62, 43A07, 43A15, 46H20. DOI: 10.4064/cm116-1-2

Abstract

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.

Authors

  • Rupert LasserInstitute 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
    e-mail

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