  Expected duality and approximation properties are shown to fail on Bergman
spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an
operator satisfying certain mapping properties, positive duality and
approximation results are proved. Such operators are constructed on generalized
Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of
Laurent series of Bergman functions is shown. This extends a classical result
on Hardy spaces of the unit disc.
