Definition:Support Functional

Definition
Let $\struct {X, \norm \cdot_X}$ be a normed vector space.

Let $\struct {X^\ast, \norm \cdot_{X^\ast} }$ be the normed dual space of $X$.

Let $x \in X$.

We say that $f \in X^\ast$ is a support functional at $x$ :


 * $(1): \quad$ $\norm f_{X^\ast} = 1$
 * $(2): \quad$ $\map f x = \norm x_X$.

Also see

 * Existence of Support Functional