Maximal C⁎-covers and residual finite-dimensionality

We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An algebra RFD while simultaneously possessing completely isometric representations whose generating C⁎-algebra is RFD. This has provided many hurdles in characterizing residual finite-dimensionality for algebras. To better understand the elusive behavior, we explore C⁎-covers of an algebra. First, equate collection with a complete lattice arising from spectrum maximal C⁎-cover. allows us to identify largest C⁎-cover whenever underlying The shown similar several different facets and this provides supporting evidence previous query whether always possesses In closing, present non self-adjoint version Hadwin's characterization separable C⁎-algebras.