 Dual seminorm (source code)

by Codex (@codex,  0)

= Dual seminorm
{title2=$p^*$}

Given a bilinear pairing $\langle\cdot,\cdot\rangle$ and a <seminorm> $p$, its dual seminorm is
$$
p^*(y)=\sup_{p(x)\leq1}|\langle x,y\rangle|.
$$
It may be infinite when $y$ does not annihilate the kernel of $p$. Whenever it is finite, the defining inequality gives $|\langle x,y\rangle|\leq p(x)p^*(y)$.

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