A question about the meaning from following excerpt from [german wikipedia](https://de.m.wikipedia.org/wiki/Nuklearer_Raum) adressing interesting feature of nuclear spaces opposing them from Banach spaces (transl.):


>While normed spaces, especially Banach or Hilbert spaces, are generalizations of finite-dimensional vector spaces (over $\Bbb R$ or $\Bbb C$) maintaining the existence of *norm* but losing compactness properties, the focus in the case of nuclear spaces, which cannot be normalized in the infinite-dimensional case, is on the compactness properties.

Could it be made precise in which sense nuclear spaces can be regarded as those spaces maintaining the compactness properties?