Gruppi e spazi vettoriali nucleari – Parte I
The aim of the course is to give a survey on the theory of nuclear spaces and nuclear groups. The nuclear spaces were introduced and studied by A. Grothendieck in the fifties, the nuclear groups by W. Banszczyk in the nineties. First we point out common properties of locally compact abelian groups and of nuclear vector spaces and we will motivate afterwards the definition of nuclear groups. The class of nuclear groups forms a Hausdorff variety of abelian groups which contains the groups mentioned above. Afterwards we will present some of the results known for nuclear groups as summability properties and duality properties.