Definition:Norm/Bounded Linear Transformation/Definition 2

Definition
Let $H, K$ be Hilbert spaces, and let $A: H \to K$ be a bounded linear transformation.

The norm of $A$, denoted $\norm A$, is the real number defined by:


 * $\norm A = \sup \set {\dfrac {\norm {A h}_K} {\norm h_H}: h \in H, h \ne \mathbf 0_H}$

Also see

 * Definition:Hilbert Space
 * Definition:Bounded Linear Transformation