Definition:Norm/Bounded Linear Functional

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

Also see

 * Equivalence of Definitions of Norm of Linear Functional


 * Bounded Linear Functional Norm is Finite where it is shown that $\norm L < \infty$.


 * Corollary of Equivalence of Definitions of Norm of Linear Functional where it is shown, for all $h \in H$, that $\size {L h} \le \norm L \norm h$.

Special cases

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