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Strongly invariant means on commutative hypergroups.

Colloq. Math. 129, 119-131 (2012)
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We introduce and study strongly invariant means m on commutative hypergroups, m(T-x phi . psi) = m(phi . T-(x) over tilde psi), x is an element of K, phi, psi is an element of L-infinity (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.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Hypergroups ; Strongly Invariant Mean ; Reiter's Condition
ISSN (print) / ISBN 0010-1354
e-ISSN 1730-6302
Quellenangaben Volume: 129, Issue: 1, Pages: 119-131 Article Number: , Supplement: ,
Publisher Institute of Mathematics, Polish Academy of Sciences
Reviewing status Peer reviewed