3 problems

Let $G$ be a locally compact group. Write $\operatorname{TLIM}(G)$ for the topological left-invariant means on $L_\infty(G)$ and $\operatorname{TIM}(G)$ for the two-sided topologic…

Let $H$ be a Hilbert space, let $U(H)$ be its unitary group, and consider invariant means on $U(H)$. A multiplicative invariant mean is an invariant mean belonging to the multiplic…

Let $\Gamma$ be a discrete abelian group, let $m\in\mathcal M_{\tau}(\Gamma)$ be an invariant mean, let $\sigma$ be a Choquet decomposition of $m$, and let…