Definition:Norm/Bounded Linear Functional/Inner Product Space

Definition
Let $\mathbb F$ be a subfield of $\C$.

Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\mathbb F$ with $V \ne \set 0$.

Let $L : V \to \mathbb F$ be a bounded linear functional.

Let $\norm \cdot$ be the inner product norm for $\struct {V, \innerprod \cdot \cdot}$.