Properties of quasi-invariant measures on topological groups and associated algebras
Let \(G\) be a topological group, \(H\) its invariant subgroup and \(\mu \) a measure defined on the completion \(Af( G,\mu) \) of the Borel \(\sigma \)-field of \(G\). Then \(\mu \) is called left-quasi-invariant provided \(\mu _{h}\) is equivalent to \(\mu \) for each \( h\in H\), where \(\mu _{h}( A) :=\mu ( h^{-1}A) \) for each \(A\in Af( G,\mu) \). The author studies: a) weakly continuous (weakly measurable) representations of a topological group \(G\) with a left-quasi-invariant measure; b) maximal ideals of a non-associative Banach algebra associated to a topological group which possesses a decreasing sequence of subgroups with left-quasi-invariant measures.
scientific article; zbMATH DE number 1331689
scientific article