most recent 30 from http://mathoverflow.net 2013-05-25T09:29:44Z http://mathoverflow.net/feeds/question/88426 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88426/mappings-preserving-convex-compactness unknown (google) 2012-02-14T12:28:21Z 2012-02-14T12:28:21Z

<p>Let $H$ be a Hilbert space.</p> <p>How can one describe continuous mappings $F:H \to H$ that satisfy the following condition:</p> <p>There exist two elements $c$, $F(c) \neq c$ and a convex compact $M$ containing $c$ and $F(c)$ such that $F(M)$ is convex.</p> <p>Of course, $F(M)$ is also compact since $F$ is continuous.</p> <p>Thank you very much in advance!</p>