Norm on a Dual Space

azdang

1. Homework Statement
X is the space of ordered n-tuples of real numbers and ||x||=max|$$\xi$$j| where x=($$\xi$$1,...,$$\xi$$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.

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matt grime

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

azdang

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

azdang

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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