Hi guys,

could you please help me with the following problem:

(e_{n}) is an orthonormal sequence on Hilbert space. Let E be a dense subset of H. ($\displaystyle E\subset H , \bar{E}=H$)

Prove that the (e_{n}) is a basis on the Hilbert space if the following stands for every $\displaystyle x \in E $:

$\displaystyle \left \| x \right \|^{2}=\sum_{n=1 }^{\infty}\left | \left \langle x, e_{n} \right \rangle \right | ^{2}$