Riesz' Representation Theorem states that every linear functional can be represented by a vector. This shows that the Dual can be ANTILINEARLY and norm preserving identified with the Hilbert Space itself.
I'm now wondering: Is it also possible (maybe in a completely different fashion) to LINEARLY and norm preserving identify the Dual (not the "Antidual") with the Hilbert Space? In any, case is there a proof for it?