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!



Reference for : a Fréchet nuclear space is Montel
Have a look at Proposition 50.2 in



> 
> F. Treves: *Topological Vectors
>  Spaces, Distributions and Kernels*,
>  Academic Press 1995 or Dover 2006
> 
> 
> 


Statement (50.12) in that proposition is precisely what you need.


