You could take the operator to be the operation of differentiation. Of course, you'll have to explain why it is (a) densely defined and (b) unbounded.
Hi i'm having trouble with this:
Consider a linear operator from a Banach space X to X. Let X=L2(0,1) (lebesgue space with p=2). Give an example of a (densely defined) linear operator A which is unbounded from X to X?