Could you please help with the following?
Let X be a normed vector space with Banach dual space X'. Let be in X' such that . Show that
is a well-defined linear map on a subspace of . Extending T to all of , show that there are such that
Conclude that, for any finite-dimensional subspace M of X',
Now, by definition, for
Now, I can show that T is well-defined and linear on the subspace .
By the Hahn-Banach theorem, I can extend this to a function such that and . But where do I go from here?