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!
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Sign up to join this communityI'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
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.
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