Definition:Second Normed Dual

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

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

We define the second normed dual, written $\struct {X^{\ast \ast}, \norm \cdot_{X^{\ast \ast} } }$ as the normed dual of $\struct {X^\ast, \norm \cdot_{X^\ast} }$.