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An example of norms that are not equivalent

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Give an example of two norms on a vector space that are not equivalent.

    2. Relevant equations

    3. The attempt at a solution

    Hi everyone,

    I know the definition for equivalent norms. I also know that norms on a finite dimensional vector space are equivalent. So clearly the vector space has to be infinitely dimensional.
    In which case can you take the normal euclidean norm and the max norm? And if not, could someone please point me in the right direction?

    Thanks for any help
  2. jcsd
  3. Apr 20, 2010 #2
    Consider C[0,1] - continuous functions on the unit interval. Try the sup norm and L1 norm.
    Of course there are a lot of different examples, depending on what stuff you are comfortable with.
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