Generating cones having no surjections [in operator spaces] - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T01:54:26Z http://mathoverflow.net/feeds/question/20351 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/20351/generating-cones-having-no-surjections-in-operator-spaces Generating cones having no surjections [in operator spaces] Ady 2010-04-05T00:57:41Z 2010-04-05T03:33:02Z <p>Is this little toy known ?</p> <p>Let $E$ be some Banach space, and let $K$ be the closed unit ball of its dual, endowed with the weak-star topology. Also, let $j:E$ $\rightarrow$ $C(K)$ be the natural embedding. Then, if $\pi$ :$E$ $\rightarrow$ $C(K)$ is onto, one must have $\left\Vert \pi-j\right\Vert$ > 1. [Applying this to $E=$ $\ell^{1}$, or to $E=C[0,1]$ (eventually, via Milutin) would be interesting, I think.]</p>