Talk:Bounded inverse theorem
The example as presented is somewhat confusing. I believe it could be improved by noting the following:
- The reason that the example space X is a not a Banach space is because it is not complete (see Completeness (topology)). (Talking about it failing to be a close subspace of l-infty seems beside the point, and confuses the issue.)
- The completion of the example space X is l-infinity. However, in this case, the map T is not onto (and thus not bijective). So, for example, the sequence is in l-infty, but is not in the range of T.