Definition:Norm/Bounded Linear Functional/Normed Vector Space/Definition 4

Definition
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.

The norm of $L$ is the infimum:


 * $\norm L = \inf \set {c > 0: \forall v \in V : \size {L v} \le c \norm v}$