If is dense then so , but is always closed so . For the other direction is the same, if then .
Hey, I have difficulties with the following question;
Let be a Hilbert space with associated inner product , and let be a linear subspace of . Define the orthogonal set of as . Show that is dense in if and only if .
I've already shown that is always a closed linear subspace of , and I am told I can use the fact that, if a given linear subspace is closed, then .
From here, I guess that I have to sow that iff the closure of is , but I can't manage to get started on either side of the iif.