Duality Theory for Covariant Systems

If (A,ρ ,G) is a covariant system over a locally compact group G, i.e. ρ is a homomorphism from G into the group of -automorphisms of an operator algebra A, there is a new operator algebra A called the covariance algebra associated with (A,ρ ,G). If A is a von Neumann algebra and ρ is σ-weakly continuous, A is defined such that it is a von Neumann algebra. If A is a C-algebra and ρ is norm-continuous A will be a C-algebra. The following problems are studied in these two different settings: 1. If A is a covariance algebra, how do we recover A and ρ? 2. When is an operator algebra A the covariance algebra for some covariant system over a given locally compact group G?