  In this paper, we study some properties of viscosity sub/super-solutions of a
class of fully nonlinear elliptic equations relative to the eigenvalues of the
complex Hessian. We show that every viscosity subsolution is approximated by a
decreasing sequence of smooth subsolutions. When the equations satisfy some
conditions on the limit at infinity, we verify that the comparison principle
holds, and as a sequence, we obtain a result about the existence of solution of
the Dirichlet problem. Using the comparison principle, we show that, under
suitable conditions, a Perron-Bremermann envelope can be approximated by a
decreasing sequence of viscosity solutions.

Analysis of PDEs;Complex Variables