It's easy to see that the sequence satisfies Parseval's identity iff for all . To prove that this happens iff the sequence is an orthonormal basis see here (the last post).
Can anyone give me some help on this one please.
Let H be a Hilbert space and Let be an orthonormal sequence for H. Write down Parseval's identity for . Show that an orthonormal basis in H if and only if it satisfies Parseval's identity.
Parseval's identity is how do i write using this identity?