\begin{definition}[Definition:Norm/Bounded Linear Functional/Normed Vector Space]
Let $\mathbb F$ be a subfield of $\C$. 
Let $\struct {V, \norm \cdot}$ be a normed vector space over $\mathbb F$ with $V \ne \set 0$.
Let $L : V \to \mathbb F$ be a bounded linear functional.
\end{definition}