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

Compactness for the d-bar - Neumann problem - a functional analysis approach