Definition:Induced Norm
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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 $Y$.
- $\norm {\, \cdot \,}_Y := \norm {\, \cdot \,}_X {\restriction_Y}$
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): $\S 1.2$: Normed and Banach spaces. Normed spaces