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Norm on a Dual Space

  • Thread starter azdang
  • Start date
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1. Homework Statement
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. Homework 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.
 

matt grime

Science Advisor
Homework Helper
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What is the definition of the dual space and its norm?
 
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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
 
84
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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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