Let $H$ be an infinite dimensional separable Hilbert space. the set $K(H)$ of all compact operators is a non-unital nuclear $C^*$-algebra which has no tracial states and the multiplier algebra of $K(H)$ is also traceless.

My quesion: do there exist other concrete non-unital nuclear $C^*$-algebras without tracial states and their multiplier algebras are also traceless?

Let $H$ be an infinite dimensional separable Hilbert space. The set $K(H)$ of all compact operators is a non-unital nuclear $C^*$-algebra which has no tracial states and the multiplier algebra of $K(H)$ is also traceless.

My question: do there exist other concrete non-unital nuclear $C^*$-algebras without tracial states such that their multiplier algebras are also traceless?