Definition:Norm/Bounded Linear Functional

Definition
Let $\GF$ be a subfield of $\C$.

Let $\struct {V, \norm {\, \cdot \,} }$ be a normed vector space over $\GF$.

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

Also known as
Since this is the norm associated with the normed dual space, it is often known as the dual norm.

Also see

 * Equivalence of Definitions of Norm of Linear Functional


 * Norm on Bounded Linear Functional is Finite
 * Corollary of Equivalence of Definitions of Norm of Linear Functional where it is shown, for all $v \in V$, that $\size {L v} \le \norm L \norm v$.


 * Definition:Bounded Linear Functional
 * Definition:Norm on Bounded Linear Transformation, of which this is a special case.