Hi guys.

Where can I find a proof that for every there exist such that for all : , and that it is unique?

I looked around in google and all I could find is a very complicated explanation about Riesz representation theorem.

please, if someone could direct me to a simple proof that shows it, that would be great.

but most importantly, the reason I posted this thread is that I just recently relized that it has a strong connection to functionals, and I would love to get a good understanding of it.

so if anyone can just explain it in simple words, or post a link to a proof that shows the uniqueness of adjoint operators and how it relates to functionals, that would be great.

I feel like I'm almost there, but I just can't get to the bottom of it.

thanks in advanced!