Why is functional calculus called functional calculus? What does functional mean in functional calculus?

Question

Given a unital Banach algebra $B$, functional calculus allows one to define $f(a)\in B$ for continuous function $f$ and $a\in B$.

A functional is a mapping from a vector space to its scalar space. But where is the functional in functional calculus? Why is it not called function calculus?

Answer 1

I have always understood the term Functional to be the noun, that is how functional is the calculus on offer. Of course, we require a priori the object of our study to be a function of some sort, represented by some algebra homomorphism for example.