Complete orthonormal system of eigenfunctions for trace-class nonnegative operator on a Hilbert space

Question

In Da Prato/Zabczyk's book "Stochastic equations in inifinite dimension" I stumbled over the following paragraph:

Let $Q$ be a trace class nonnegative operator on a Hilbert space $U$. [...] Note that there exists a complete orthonormal system $\{e_k\}$ in $U$ and a bounded sequence of nonnegative real numbers $\{\lambda_k\}$ such that $$ Qe_k = \lambda_k e_k.$$ Why is that?