\begin{definition}[Definition:Evaluation Linear Transformation/Normed Vector Space]
Let $\Bbb F \in \set {\R, \C}$. 
Let $\struct {X, \norm \cdot_X}$ be a normed vector space over $\Bbb F$.
Let $\struct {X^\ast, \norm \cdot_{X^\ast} }$ be the normed dual of $\struct {X, \norm \cdot_X}$.
Let $\map L {X^\ast, \Bbb F}$ be the set of linear functionals on $X^\ast$. 
For each $x \in X$, define $x^\wedge : X^\ast \to \Bbb F$ by: 
:$\map {x^\wedge} f = \map f x$
Then we define the '''evaluation linear transformation from $X$ into $X^{\ast \ast}$''' as the function $J : X \to \map L {X^\ast, \Bbb F}$ defined by:
:$\map J x = x^\wedge$
for each $x \in X$.
\end{definition}