= Absolutely summable sequence space
{title2=$\ell^1=\{x:\sum_n|x_n|<\infty\}$}
= l1 sequence space
{c}
{synonym}
The <Banach space> $\ell^1$ consists of absolutely summable scalar sequences, with <norm> $\|x\|_1=\sum_n|x_n|$. Its continuous dual is $\ell^\infty$, under the pairing $\sum_nx_ny_n$. Finitely supported sequences are <norm> dense, which identifies a <linear functional> from its values on coordinate vectors. The <space of sequences converging to zero> inside this dual is a <norming subspace> of infinite codimension.
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