Definition:Bounded Linear Functional/Normed Vector Space

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

Let $\struct {X, \norm \cdot}$ be a normed vector space over $\mathbb F$.

Let $f : X \to \mathbb F$ be a linear functional.

We say that $f$ is a bounded linear functional :


 * there exists $C > 0$ such that $\cmod {\map f x} \le C \norm x$ for each $x \in X$.