Let X be a banach space. When does exist a Banach space Y such that X is isometrical isomorph to Y*? When does Y be unique? I'm wondering this because I would like to use a weak* topology over X.
If the dimension is finite, then everything is trivial.
If X is reflexive, then Y must be reflexive (if Y exists). So the claim should be Y=X* But even if I prove the claim, this won't help me since weak topology* is equivalent to weak topology under those conditions.