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Point derivations on the L¹-algebra of polynomial hypergroups

100%

Lasser R.

Colloquium Mathematicum

2009

tom 116

nr 1

15-30

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.

Amenability and weak amenability of l¹-algebras of polynomial hypergroups

100%

Lasser R.

Studia Mathematica

2007

tom 182

nr 2

183-196

We investigate amenability and weak amenability of the l¹-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, we prove amenability for the hypergroup induced by the Chebyshev polynomials of the first kind.

Strongly invariant means on commutative hypergroups

63%

Lasser R. , Obermaier J.

Colloquium Mathematicum

2012

tom 129

nr 1

119-131

We introduce and study strongly invariant means m on commutative hypergroups, $m(T_{x}φ · ψ) = m(φ · T_{x̃}ψ)$, x ∈ K, $φ,ψ ∈ L^{∞}(K)$. We show that the existence of such means is equivalent to a strong Reiter condition. For polynomial hypergroups we derive a growth condition for the Haar weights which is equivalent to the existence of strongly invariant means. We apply this characterization to show that there are commutative hypergroups which do not possess strongly invariant means.