Let $f:\mathcal l^{\infty} \to \mathbb R$ be a linear functional such that $f(x)\ge 0$ whenever $x \in \mathcal l^{\infty} $ is a sequence with non-negative terms ; then is $f$ continuous ?
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Martin Sleziak
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Do you, by $l^\infty$, mean the space of bounded sequences? – Matias Heikkilä Apr 18 '16 at 15:09
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@MatiasHeikkilä : Yes , indeed the space of bounded sequences – Apr 18 '16 at 15:09
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You might want to have a look at this: http://math.stackexchange.com/a/99242/66856 – Matias Heikkilä Apr 18 '16 at 15:34