Could someone explain me why, given a hilbert space, its orthogonal complement is always the one-element set containing 0, i.e.
Drexel, I think the question (b) concerns me. I suppose I must use something that has to do with the completeness of the hilbert space. But I guess TheEmptySet's answer is ok.
For example, I need this property when I want to prove that if S is a nonempty set, dense in an inner-product space X, then .