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Norm on a Dual Space

  1. Mar 12, 2009 #1
    1. The problem statement, all variables and given/known data
    X is the space of ordered n-tuples of real numbers and ||x||=max|[tex]\xi[/tex]j| where x=([tex]\xi[/tex]1,...,[tex]\xi[/tex]n). What is the corresponding norm on the dual space X'?


    2. Relevant equations



    3. The attempt at a solution
    I think the answer is that ||x*||=|x_1|+...+|x_n| , but I'm not sure if that's correct or how to show it. Any ideas? Thanks so much.
     
  2. jcsd
  3. Mar 12, 2009 #2

    matt grime

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    What is the definition of the dual space and its norm?
     
  4. Mar 12, 2009 #3
    Well, I know the dual space,X', is the set of all bounded linear functionals on X and the norm on that space is:
    ||f||=sup|f(x)|/||x|| for x in X and x not equal to 0
    or
    ||f||=sup|f(x)| for x in X and ||x||=1
     
  5. Mar 14, 2009 #4
    Hey guys, although Matt advised me to think about the definitions, I'm still confused how to apply them to this problem. Any ideas? Thanks so much.
     
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