Definition:Induced Norm

Definition
Let $\struct {X, \norm {\, \cdot \,}_X}$ be a normed vector space.

Let $Y \subseteq X$ be a subspace.

Then the induced norm (on $Y$) is defined as the restriction of $\norm {\, \cdot \,}_X$ to $Y$.


 * $\norm {\, \cdot \,}_Y := \norm {\, \cdot \,}_X {\restriction_Y}$