Reference request for the proof of the Brodskii–Milman fixed point theroem for isometries

91 Views Asked by At

Can any one help me to access the paper

M.S Brodskii and D.P Milman, On the center of a convex set, Dokl. Akad. Nauk SSSR 59 (1948) 837–840 in Russian?

or to prove the theorem

If $K$ is a weakly compact, bounded convex subset of a Banach space with normal structure, then there exists $x_0\in K$ such that $T(x_0)=x_0$ for all surjective isometry $T:K\to K$. That is there is a common fixed point for the family of surjective isometris on $K$.

Thank you.