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

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 $C_{0}(\Omega)$‎
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