The one thing the duality section was connected to was Riesz representation theorem. Riesz states every finite linear functional φ has a unique vector f, such that for all v, φ(v) = <v,f>. It gives an isomorphism from functionals to vectors for a given norm, as the function is just multiplication with the vector.
It’s not tied to the section on duals in the text, but the section on duals lets you appreciate the result more.
The one thing the duality section was connected to was Riesz representation theorem. Riesz states every finite linear functional φ has a unique vector f, such that for all v, φ(v) = <v,f>. It gives an isomorphism from functionals to vectors for a given norm, as the function is just multiplication with the vector.
It’s not tied to the section on duals in the text, but the section on duals lets you appreciate the result more.