Definition:Norm/Bounded Linear Transformation/Definition 2

Definition
Let $\HH$ and $\KK$ be Hilbert spaces.

Let $A: \HH \to \KK$ be a bounded linear transformation.

The norm of $A$ is the real number defined and denoted as:


 * $\norm A = \sup \set {\dfrac {\norm {A h}_\KK} {\norm h_\HH}: h \in \HH, h \ne \mathbf 0_\HH}$

Also see

 * Definition:Hilbert Space
 * Definition:Bounded Linear Transformation