We have learnt the following two theorems (Functional Analysis by J.B. Conway):
and
Where $X$ is a normed space and $M$ is a closed subspace.
And we were told that there is a similar result (May be a theorem) when $X$ is a Hilbert Space.
So could you help me to verify that..
I know in Hilbert space we can have $M^{\perp}=\{ x\in X: <x,m>=0, \forall m\in M \}$
I'm not sure whether my question has an exact answer. But I appreciate your opinion.