Definition:Norm/Bounded Linear Functional

Definition
Let $H$ be a Hilbert space, and let $L$ be a bounded linear functional on $H$.

Definition 4
As a consequence of definition $(4)$, we have for all $h \in H$ that $\size {L h} \le \norm L \norm h$.

As $L$ is bounded, it is assured that $\norm L < \infty$.

Also see

 * Equivalence of Definitions of Norm of Linear Functional

Special cases

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