\begin{definition}[Definition:Bounded Linear Functional/Inner Product Space]
Let $\mathbb F$ be a subfield of $\C$. 
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\mathbb F$.
Let $\norm \cdot$ be the inner product norm for $\struct {V, \innerprod \cdot \cdot}$. 
Let $f : V \to \mathbb F$ be a linear functional.
We say that $f$ is a '''bounded linear functional''' {{iff}}:
:there exists $C > 0$ such that $\cmod {\map f v} \le C \norm v$ for each $v \in V$.
\end{definition}