I'm looking for a reference to cite regarding the property presented in the title: "Closed and bounded sets of a nuclear Fréchet space are compact"
Thank you in advance for the help!
I'm looking for a reference to cite regarding the property presented in the title: "Closed and bounded sets of a nuclear Fréchet space are compact" Thank you in advance for the help! 


Have a look at Proposition 50.2 in
Statement (50.12) in that proposition is precisely what you need. 


Maybe not in a single theorem, but you can go for Cor1 in Section 33 and Cor3 in Section 50 in Treves book. 


does Wikipedia qualify as a reference? for a historical overview, see A pedagogical history of compactness 

