Residually finite-dimensional operator algebras
residual finite-dimensionality, non-selfadjoint operator algebras, tensor algebras, C⁎-covers
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.
Clouatre, R. & Ramsey, C. (2019). Residually finite-dimensional operator algebras. Journal of Functional Analysis 277 (8), 2572-2616. https://doi.org/10.1016/j.jfa.2018.12.016
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