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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
5
votes
Dual norm of a subspace of $\ell_\infty^3$
This answer uses a lot of the same ideas as Onur Oktay's answer, but I believe corrects some problems with it. If we define $\mathbf{e}_1 = (1,0)$, $\mathbf{e}_2 = (0,1)$, $\mathbf{u} = (1,1)/\sqrt{2} …
14
votes
How hard (P, NP, NP-hard) is it to compute Schur norms of matrices (as multipliers)?
It turns out that this norm can be computed efficiently (i.e., it is in $P$). This wasn't known at the time that the Davidson paper (originally linked in a comment above) was written, which is why it …