1. Non-normable functional spaces

1.1 Wielandt's lemma

Banach spaces provide a more general framework than Hilbert spaces, one that contains a large part of functional analysis, since, as we have seen, many functional spaces have a natural complete norm (cf. article ).

However, function spaces ${\mathcal{C}}^{\infty }$ cannot be provided with a natural Banach space structure. This stems from a very simple equation: if f is a differentiable function, we have :

So if xml...