2018/05/31 by Clouâtre, Raphaël, Ramsey, Christopher · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1806.00038
We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional C^*-algebras, in the non-selfadjoint setting we show that an additional level of flexibility must be allowed. Motivated by this peculiarity, we consider a natural non-selfadjoint notion of residual finite-dimensionality. We identify sufficient conditions for the tensor algebra of a C^*-correspondence to enjoy this property. To clarify the connection with the usual self-adjoint notion, we investigate the residual finite-dimensionality of the minimal and maximal C^*-covers associated to an operator algebra.