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I have made functional and operator primarily about the meanings of these in higher-order logic, where these terms are used exclusively and unqualified. I have accordingly split off linear functional from functional; linear operator (redirecting to linear map) was already separate from operator (which was only for disambiguation). I have also checked each incoming link to functional or operator (or a plural form) to link instead to linear functional or linear operator when appropriate.
That said, there are such things as nonlinear functionals and operators on abstract vector spaces, things which are also not functionals or operators in the type-theoretic sense. Possibly we would want pages such as nonlinear functional and nonlinear operator to cover these. (Compare nonassociative algebra, which covers a topic more general than what is covered at associative algebra but also could not be covered at simply algebra.)
I did not know what to do with the phrase ‘various discretised versions are interesting in finite geometries as well as numerical analysis’. Are these linear functionals, type-theoretic functionals, both, or neither?
Okay, I have added to the Disambiguation-paragraph the sentence
There is also the notion of functional as “function on infinite-dimensional manifolds”, for these see at nonlinear functional.
and am creating a stub for nonlinear functional now, cross-linking it with action functional.
OK, I had let ‘action functional’ and the like link to the type-theoretic notion, but I guess that these have now been abstracted enough that (like the linear functionals on vector spaces) they are no longer only applied to spaces of paths (which are themselves functions).
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