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 ?
2026-04-19 17:16:43.1776619003
$f \in \mathcal l^{\infty}{'} $ ; $f(x)\ge 0$ whenever $x \in \mathcal l^{\infty} $ is a sequence of non-negative terms ; is $f$ bounded?
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