Describe dual space of $C[0,1]$

Asked Nov 08 '12 at 08:12

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I am stuck in this problem.

Describe the dual space of $C[0,1]$, where $C[0,1]$ is the Banach space of all real continuous functions on $[0,1]$ induced norm $$ \|x\|_{\max}=\sup_{t\in [0,1]}|x(t)|\quad \forall x\in C[0,1]. $$

Thank you for all helping.

asked Nov 08 '12 at 08:12

blindman

3,117

1

Two links that will help: 1. Riesz representation theorem 2. Riemann-Stieltjes integral – Nov 08 '12 at 08:33
1

Look up the Riesz representation theorem. – copper.hat Nov 08 '12 at 08:33

Describe dual space of $C[0,1]$

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