\begin{definition}[Definition:Reflexive Space]
Let $\struct {X, \norm \cdot_X}$ be a normed vector space.
Let $\struct {X^{\ast \ast}, \norm \cdot_{X^{\ast \ast} } }$ be the second normed dual of $\struct {X, \norm \cdot_X}$.
Let $J : X \to X^{\ast \ast}$ be the evaluation linear transformation.
We say that $X$ is '''reflexive''' {{iff}}:
:$J$ is an isometric isomorphism.
\end{definition}