The Etymology of the Term "Nuclear Operators"

Question

Grothendieck in his "Résumé " on the metric theory of topological tensor products, defines the notion of nuclear operators on Banach spaces. My question is, is anyone aware as to why these are known as nuclear operators? Of course they are an extension of the trace class operators, say in the Hilbert space setting, but I have never truly understood why they are called nuclear. Did it perhaps to do with nuclear conflict in the 1950s (when this paper was published)? I know Grothendieck was known for political activism and opposition to war. Sorry if these are silly guesses, I am unable to find anything on this choice of name, and am puzzled by it.

Answer 1

amsmath's comment "nucleus = kernel..." is an apt one, as the "Schwartz kernel theorem" / $\,\ll\,$Théorème des noyaux$\,\gg\,$ in French ¹, is the etymological source of the terms Nuclear operator and Nuclear space.

A short synopsis
Grothendieck answered a question put forward to him by L. Schwartz, being his thesis advisor then. He clarified the origin of a locally-convex topology, defined by Schwartz within distribution theory and till then opaque ², on the tensor product $\,\mathscr D'\otimes F\,$ which is naturally a subspace of $\,\mathscr L(\mathscr D,F)$.
Grothendieck introduced the projective tensor product $\otimes_\pi$ and coined the term nuclear operator / $\ll$application nucléaire$\gg$ in French, for elements in $\mathscr L(E,F)$ arising from $E'\hat{\otimes}_\pi F$, where $E,F$ are locally-convex spaces. Previously such operators had only been analysed in the case $E,F$ being Banach spaces.

Furthermore,
he introduced the injective tensor product topology $\otimes_\epsilon$, and defined a space $\mathcal{N}$ as nuclear if $\mathcal{N}\!\otimes_\pi\! E$ and $\mathcal{N}\!\otimes_\epsilon\! E$ coincide as locally-convex spaces for every $E$ (in fact, it is sufficient to check the equality for $E=\ell^1$, the summable sequences). All the prominent spaces in distribution theory are nuclear.
When restricted to Banach spaces, nuclearity is not a fruitful concept since no infinite-dimensional Banach space is nuclear.

Regarding your conjecture
that 'nuclear' stems from the 1950 politics context, I'd like to add that Grothendieck's solutions were like a nuclear blow up$-$not politically or else, but in the further development of functional analysis. He turned the field upside down, then moved on into Algebraic geometry.

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¹ See Résumé par Grothendieck, Ann. Institut Fourier on page 99

² Search for 'nuclear', or start reading on page 8 in
https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Mathematics/chap3.pdf