Using that $||f+g||^{2}=||f||^{2}+2Re(f,g)+{||g||}^{2}$ for any pair of elements in a Hilbert space, establish the parallelogram law.
I believe the proof is this:
How do I prove the parallelogram law?
And there is also a Wiki-proof likewise (same one it looks like). But, this equation seems a little different than the one in my question...
is it the same? Their equation reads differently and I can't see how they're equivalent.
But, I'm surely confused with the notation $2Re(f,g)$; does this mean $2$ times the "real part" of $(f,g)$? What is the real part of $(f,g)?$