closed complement - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T06:49:40Z http://mathoverflow.net/feeds/question/116225 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116225/closed-complement closed complement Prasanth 2012-12-13T02:13:15Z 2012-12-13T04:02:52Z <p>How can we show that $c_0$ has no closed complement in $l^\infty$. Similarly $C([0,1])$ has no closed complement in $B([0,1])$</p> http://mathoverflow.net/questions/116225/closed-complement/116235#116235 Answer by Bill Johnson for closed complement Bill Johnson 2012-12-13T04:02:52Z 2012-12-13T04:02:52Z <p>For the first question, see Theorem 2.5.5 in the book of Albiac and Kalton. The second question is immediate from the first and the easy fact that $C[0,1]$ has a complemented subspace isometric to $c_0$.</p>