G. Racher
Injective Modules and Amenable Groups
Preprint series: ESI preprints

MSC:

43A07 Means on groups, semigroups, etc.; amenable groups

46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

18G05 Projectives and injectives, See also {13C10, 13C11, 16D40,

Abstract: We show that a locally compact group is amenable if and only if
it admits a (nontrivial) injective Banach module which is reflexive
as a Banach space, generalizing work by H.G.~Dales, M.~Daws, H.L.~Pham,
P.~Ramsden, and M.E.~ Polyakov.


Keywords: Amenable groups, injective Banach modules, weak compactness