A relative bicommutant theorem: the stable case of Pedersen's question

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In 1976, D. Voiculescu proved that every separable unital sub-C*-algebra of the Calkin algebra is equal to its (relative) bicommutant. In his minicourse (see reference), G. Pedersen asked in 1988 if Voiculescu's theorem can be extended to a simple corona algebra of a σ-unital C*-algebra. In this note, we answer Pedersen's question for a stable σ-unital C*-algebra.