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

(x f )′ – x f ′ = f

So if xml...

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Mathematics