Invariant means on Abelian groups capture complementability of Banach spaces in their second duals

Adam P. Goucher, Tomasz Kania

Let $X$ be a Banach space. Then $X$ is complemented in the bidual $X^{\ast \ast }$ if and only if there exists an invariant mean ${\ell }_{\infty }(G,X)\to X$ with respect to a free Abelian gro…