Category:Definitions/Quotient Norms

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Quotient Norms.
Related results can be found in Category:Quotient Norms.


Let $X$ be a normed vector space.

Let $N$ be a closed linear subspace of $X$.

Let $X/N$ be the quotient vector space of $X$ modulo $N$.

Let $\pi : X \to X/N$ be the quotient mapping associated with $X/N$.


We define the quotient norm $\norm \cdot_{X/N}$ by:

$\ds \norm {\map \pi x}_{X/N} = \inf_{z \in N} \norm {x - z}$

for each $x \in X$.

Pages in category "Definitions/Quotient Norms"

This category contains only the following page.