Definition:Norm/Bounded Linear Transformation/Definition 1

From ProofWiki
Jump to navigation Jump to search

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:

$\norm A = \sup \set {\norm {A h}_K: \norm h_H \le 1}$


Also see