Frechet Derivative: Why bounded (linear) operator? Why do we want the frechet derivative to be a _bounded_ linear operator? (This meant more as a collecting ideas - I know bounded operators behave fine but that would exclude alot of examples such as the unbounded differentiation operator)

By Norbert:


> Study of unbounded operators that arise in practice is a kind of hack-work (imho) , so biulding a general theory for them is pointless as you can't say much useful about these objects.