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Point derivations on the L 1 -algebra of polynomial hypergroups. (English) Zbl 1167.43007
Summary: 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.

MSC:
43A62Hypergroups (abstract harmonic analysis)
43A07Means on groups, semigroups, etc.; amenable groups
43A15L p -spaces and other function spaces on groups, semigroups, etc.
46H20Structure and classification of topological algebras