Does 'functional' mean "relating to functions" or "a mapping from a space to its scalars"?
2026-04-11 13:05:35.1775912735
In "Functional Analysis," is the word "Functional" an adjective, or a noun?
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Considering one of the foundational results of functional analysis is the Banach-Steinhaus Theorem, I think it's safe to say that functional here means 'relating to functions'.
In practice, however, I'd say a good analogy would be infinite-dimensional linear algebra. So there should be a caveat about 'relating to linear functions', but they need not be functionals (ie, mapping to scalars).