# Is the C*-algebra of bounded operators simple?

Is there any condition on the Hilbert space $\mathcal{H}$ (if $\mathcal{H}$ if infinite-dimensional) such that the C*-algebra of bounded operators on $\mathcal{H}$ - $\mathcal{L}(\mathcal{H})$ - is simple ?

A $C^{\star}$ - algebra is simple if it has no nontrivial closed ideals.
If $H$ is an infinite-dimensional Hilbert space then the ideal of compact operators is a nontrivial closed ideal of $L(H)$. So, $L(H)$ is not simple.