  We discuss compactness of the d-bar-Neumann operator in the setting of
weighted L^2-spaces on C^n.$ For this purpose we use a description of
relatively compact subsets of L^2- spaces. We also point out how to use this
method to show that property (P) implies compactness for the d-bar-Neumann
operator on a smoothly bounded pseudoconvex domain and mention an abstract
functional analysis characterization of compactness of the d-bar-Neumann
operator.
