Finite dimensional approximations in operator algebras

A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD algebras in terms their state space, and moreover show that an only every representation can approximated by ones the point weak topology. This version theorem Exel Loring for C⁎-algebras. Moreover, we construct example which approximation strong topology not possible. As consequence, maximal C⁎-algebra generated this RFD. answers questions Clouâtre Ramsey Dor-On.