Strongly invariant means on commutative hypergroups

Rupert Lasser, and Josef Obermaier. "Strongly invariant means on commutative hypergroups." Colloquium Mathematicae 129.1 (2012): 119-131. <http://eudml.org/doc/283923>.

@article{RupertLasser2012,
abstract = {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.},
author = {Rupert Lasser, Josef Obermaier},
journal = {Colloquium Mathematicae},
keywords = {hypergroups; strongly invariant mean; Reiter's condition},
language = {eng},
number = {1},
pages = {119-131},
title = {Strongly invariant means on commutative hypergroups},
url = {http://eudml.org/doc/283923},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Rupert Lasser
AU - Josef Obermaier
TI - Strongly invariant means on commutative hypergroups
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 119
EP - 131
AB - 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.
LA - eng
KW - hypergroups; strongly invariant mean; Reiter's condition
UR - http://eudml.org/doc/283923
ER -