Could someone give me a hand on this problem? I want to show that the set in complete in
I tried to show that any convergent sequence in must have its limit in which means is closed in a complete space, but I failed to do this.
Presumably is . Note then that since is itself, you have that a given subspace is complete if and only if it's closed. But, evidently is closed since the mapping is a continuous (linear functional) map , and is the preimage of the closed set under this map.