A unitarization process for some non-locally compact topological groups (Q1323438)

The notion of Polish environment of quasi invariance (for short: a PEQI) for a non-locally compact topological group is introduced, which generalizes in some sense the notion of Wiener-Lie group as it is shown by giving some examples among current groups. A non-locally compact topological group \(G\) equipped with a PEQI has a left regular unitary representation; it is proved that there exists a unitarization process which associates a cyclic continuous unitary representation of \(G\) with each locally bounded representation of the PEQI.