I have found a few questions similar to this one, namely If $M$ is a closed subspace of an Hilbert space $H$, then $M^{\perp\perp}=M$, but I am not assuming that $M$ is closed, so I believe this warrants a separate question. I know that I would like to use the orthogonal composition theorem, but I am not sure how to arrive there. Any hints for what proof approach I should take are appreciated. Is it as simple as a double inclusion proof?
2026-03-25 19:06:18.1774465578
If $M$ is a subspace of a Hilbert space, then $(M^\bot)^\bot$ is the closure of $M$.
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