On closures of infinite-dimensional groups in unitary representations
Consider a topological group $G$ and its unitary representation $\rho$. Consider the closure of $\rho(G)$ in the weak operator topology. Then we get a compact semigroup with separately continuous multiplication. The purpose of talk is an introduction to problems of this type for infinite
dimensional groups. I hope to discuss briefly the similar problem for measure preserving actions of groups and non-singular actions on measure spaces (we do not suppose any preliminary knowledge of representation
theory).
