I am wondering if a norm is an example of an element of the second dual space? It takes in functionals and spits out a number.
I am trying to have some intuition for this so I have been reading posts on it but I didn’t see any concrete examples.
What I mean is, I have the following in mind:
We have the field which are numbers/vectors . Ex: 1, (1,2,3)
We have the dual space which are functions. Ex: f(x)=x^2
We have the second dual space which are functionals that take in functionals and create an element of the field. Ex: norms?
Or maybe I am way off here.... :/
Edit: Could an example be a derivative evaluated at a number? The derivative takes in a function and then generates a number in the field? I’m sorry if I’m off again here.... I am struggling to understand how a function can take in a function and create a number.