# The hermitian element $h=\sum_{n=1}^\infty \frac{p_{n}}{3^{n}}$ generates $C_{0}(\Omega)$‎

‎Please help me to solve the following problem‎ :

Let $\Omega$ be a locally compact Hausdorff space‎, ‎and suppose that the $C^{*}$-algebra $C_{0}(\Omega)$ is generated by a sequence of projections $(p_{n})_{n=1}^\infty$‎.

Then the hermitian element $h=\sum_{n=1}^\infty \frac{p_{n}}{3^{n}}$ generates $C_{0}(\Omega)$‎

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An ‎element ‎‎$‎a‎\in A‎$ is hermitian or self-adjoint if ‎$‎a=‎a‎‎^{‎*‎}‎$‎‎ –  Ali Qurbani Jan 17 '13 at 13:11
‎$C_{0}(X)=\{f\in C(X)~|~f~vanishes~at~infinity \}$ –  Ali Qurbani Jan 17 '13 at 13:13
Can you pose this as a question? –  Elements in Space Jan 18 '13 at 7:11