quotient norm

Let V be a normed vector spacePlanetmathPlanetmath with norm . Let M be a closed subspace of V and V/M the quotient vector spaceMathworldPlanetmath.

The norm induces a norm V/M in V/M, called the quotient norm, given by


Theorem - V/M is a norm in V/M iff M is closed in V.

Title quotient norm
Canonical name QuotientNorm
Date of creation 2013-03-22 17:22:58
Last modified on 2013-03-22 17:22:58
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 5
Author asteroid (17536)
Entry type Definition
Classification msc 46B99