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Zbl 1167.43007
Lasser, Rupert
Point derivations on the $L^1$-algebra of polynomial hypergroups. (English)
[J] Colloq. Math. 116, No. 1, 15-30 (2009). ISSN 0010-1354; ISSN 1730-6302/e

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 2000:: *43A62 Hypergroups (abstract harmonic analysis)
43A07 Means on groups, etc.
43A15 Lp-spaces and other function spaces on groups, etc.
46H20 Structure and classification of topological algebras

Keywords: orthogonal polynomials; hypergroups; point derivations; amenability

Cited in: Zbl 1191.43005

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