We prove a double commutant theorem for separable subalgebras of a wide class of corona C*-algebras, largely resolving a problem posed by Pedersen in 1988. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu later proved a C*-algebraic double commutant theorem for subalgebras of the Calkin algebra. We prove a similar result for subalgebras of a much more general class of so-called corona C*-algebras.

中文翻译：

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可分离 C*-代数冠冕中的双相对交换子

我们证明了一类广泛的电晕的可分离子代数的双交换定理C*-algebras，主要解决了 Pedersen 在 1988 年提出的一个问题。双交换子定理起源于 von Neumann，其开创性成果发展成为现在称为 von Neumann 代数理论的整个领域。Voiculescu 后来证明了一个C*-Calkin 代数子代数的代数双交换定理。我们为更一般的所谓电晕类的子代数证明了类似的结果C*-代数。