all norms are not equivalent

Let V be the vector space of continuous functionsMathworldPlanetmathPlanetmath [-1,1] that are differentiableMathworldPlanetmathPlanetmath at 0. Then we can define norms




It is not difficult to find a sequence of functions f1,f2, in V such that

  1. 1.

    fk(0)=k for k=1,2,,

  2. 2.


Then fk=1, and fk=1+k, so there is no C>1 such that


and and cannot be .

Title all norms are not equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath
Canonical name AllNormsAreNotEquivalent
Date of creation 2013-03-22 15:36:11
Last modified on 2013-03-22 15:36:11
Owner matte (1858)
Last modified by matte (1858)
Numerical id 6
Author matte (1858)
Entry type Example
Classification msc 46B99