Order structure on certain classes of ideals in group algebras and amenability
Copyright policy )Order structure on certain classes of ideals in group algebras and amenability
LetGbe a separable, locally compact group and let d(G) be the set of all closed left ideals inL1(G) which have the formJμ= {f−f∗ μ:f∈L1(G)}−for some discrete probability measure μ. It is shown that if d(G) has a unique maximal element with respect to the order structure by set inclusion, thenGis amenable. This answers a problem of G.A. Willis. We also examine cardinal numbers of the sets of maximal elements in d(G) for nonamenable groups.
Means on groups, semigroups, etc.; amenable groups, amenable, locally compact group, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., measure algebra, \(L^1\)-algebras on groups, semigroups, etc.
Means on groups, semigroups, etc.; amenable groups, amenable, locally compact group, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., measure algebra, \(L^1\)-algebras on groups, semigroups, etc.
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