Relative double commutants in coronas of separable C*-algebras

TL;DR

This paper establishes a double commutant theorem for separable subalgebras within a broad class of corona C*-algebras, extending classical results and resolving a longstanding open problem.

Contribution

It generalizes the double commutant theorem to corona C*-algebras, broadening the scope beyond von Neumann algebras and the Calkin algebra.

Findings

Proves a double commutant theorem for corona C*-algebras.

Extends classical von Neumann and Voiculescu results.

Resolves a problem posed by Pedersen.

Abstract

We prove a double commutant theorem for separable subalgebras of a wide class of corona C*-algebras, largely resolving a problem posed by Pedersen. 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.