Definition:Bounded Linear Transformation

Definition
Let $H, K$ be Hilbert spaces.

Let $A: H \to K$ be a linear transformation.

Then $A$ is a bounded linear transformation


 * $\exists c > 0: \forall h \in H: \left\Vert{A h}\right\Vert_K \le c \left\Vert{h}\right\Vert_H$

Also see

 * Definition:Norm on Bounded Linear Transformations, an important concept for a bounded linear transformation
 * Definition:Space of Bounded Linear Transformations


 * Continuity of Linear Transformations: a linear transformation between Hilbert spaces is bounded it is continuous.