Let $A$ be a separable $C^*$-algebra. Can $A$ embedded into a separable, simple $C^*$-algebra?
2026-04-09 06:11:11.1775715071
Embedding of separable $C^*$-algebra
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In B. Blackadar, Weak expectations and nuclear C -algebras. Indiana Univ. Math. J. 27 (1978), 1021-1026. Blackadar shows that every separable subalgebra of a simple $C^*$-algebra is contained is a simple separable $C^*$-subalgebra of $A$. In particular, every separable $C^*$-algebra can be embedded into a simple separable $C^*$-algebra (since it can be embedded into the Calking algebra).