It is idle curiosity that makes me ask so apologies for no motivation.
Let $X$ be an infinite-dimensional, closed subspace of $\ell_\infty$. Can we find a non-zero element $x\in X$ such that $x(n)\geqslant 0$ for all $n$?
It is idle curiosity that makes me ask so apologies for no motivation.
Let $X$ be an infinite-dimensional, closed subspace of $\ell_\infty$. Can we find a non-zero element $x\in X$ such that $x(n)\geqslant 0$ for all $n$?
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