Definition:Normed Dual Space

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

Let $X^\ast$ be the set of bounded linear functionals on $X$.

Let $\norm \cdot_{X^\ast}$ be the norm on bounded linear functionals.

We say that $\struct {X^\ast, \norm \cdot_{X^\ast} }$ is the normed dual space of $X$.