For several residually finite-dimensional operator algebras, including the non-commutative disc algebra, no minimal residually finite-dimensional C*-cover exists.
Arveson, Subalgebras of C∗-algebras, Acta Math
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Couniversality for C*-algebras of residually finite-dimensional operator algebras
For several residually finite-dimensional operator algebras, including the non-commutative disc algebra, no minimal residually finite-dimensional C*-cover exists.