User manuel larenas - MathOverflowmost recent 30 from http://mathoverflow.net2013-05-24T19:46:10Zhttp://mathoverflow.net/feeds/user/26704http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/107804/a-continuous-linear-functional-on-l-inftyr-that-vanishes-on-crA continuous linear functional on $L^\infty(R)$ that vanishes on $C(R)$.Manuel Larenas2012-09-21T21:05:47Z2012-09-22T01:01:47Z
<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>