Amenability, Reiter's condition and Liouville property

We show that the Liouville property and Reiter's condition are equivalent for semigroupoids. This result applies to semigroups as well as semigroup actions. In the special case of measured groupoids and locally compact groupoids, our result proves Kaimanovich's conjecture of the equivalenc...

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Bibliographic Details
Published inJournal of functional analysis Vol. 274; no. 12; pp. 3291 - 3324
Main Authors Chu, Cho-Ho, Li, Xin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2018
Subjects
Amenability
Liouville property
Reiter's condition
Semigroupoid
secondary
Semigroupoid
Liouville property
Amenability
Reiter's condition
primary
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Summary:We show that the Liouville property and Reiter's condition are equivalent for semigroupoids. This result applies to semigroups as well as semigroup actions. In the special case of measured groupoids and locally compact groupoids, our result proves Kaimanovich's conjecture of the equivalence of amenability and the Liouville property.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2018.03.014