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Strongly invariant means on commutative hypergroups.
Colloq. Math. 129, 119-131 (2012)
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
Journal
Colloquium Mathematicum
Quellenangaben
Volume: 129,
Issue: 1,
Pages: 119-131
Publisher
Institute of Mathematics, Polish Academy of Sciences
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)