Double orthogonal complement
= Double orthogonal complement
{title2=$F^{\perp\perp}$}
For a linear subspace $F$ of a <Hilbert space>,
$$
F^{\perp\perp}=\overline F.
$$
Thus $F=F^{\perp\perp}$ exactly when $F$ is closed.
= Double orthogonal complement
{title2=$F^{\perp\perp}$}
For a linear subspace $F$ of a <Hilbert space>,
$$
F^{\perp\perp}=\overline F.
$$
Thus $F=F^{\perp\perp}$ exactly when $F$ is closed.