Definition:Norm/Bounded Linear Transformation/Definition 2

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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