User manuel larenas - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T19:46:10Z http://mathoverflow.net/feeds/user/26704 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107804/a-continuous-linear-functional-on-l-inftyr-that-vanishes-on-cr A continuous linear functional on $L^\infty(R)$ that vanishes on $C(R)$. Manuel Larenas 2012-09-21T21:05:47Z 2012-09-22T01:01:47Z <p>Intuitively, I want to construct the functional F in this way:</p> <p>$$F(f)=\lim_{x\rightarrow 0+}f(x)-\lim_{x\rightarrow 0-}f(x)$$</p> <p>for $f\in L^\infty$. I know this is not well defined so I'd like to find a way to use this idea. Maybe find an extension using Hahn-Banach, etc.</p>