Point derivations on the L1-algebra of polynomial hypergroups

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Abstract

We investigate whether the L1-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 L1-algebras of hypergroups have properties (connected with amenability) that are very different from those of groups.

Original languageEnglish
Pages (from-to)15-30
Number of pages16
JournalColloquium Mathematicum
Volume116
Issue number1
DOIs
StatePublished - 2009

Keywords

  • Amenability
  • Hypergroups
  • Orthogonal polynomials
  • Point derivations

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