dual space

The dual space of a Banach space X is the vector space of continuous linear functions X→ℝ, which are called functionals. Similar notation is used for duality pairing between the Banach space X and its dual space X': ⟨u,v⟩ is the result of applying the functional u∈X' to v∈X: ⟨u,v⟩=u(v) explicitly uses the fact that u is a function X→ℝ.