  We focus on two problems relating to the question of when the product of two
posinormal operators is posinormal, giving (1) necessary conditions and
sufficient conditions for posinormal operators to have closed range, and (2)
sufficient conditions for the product of commuting closed-range posinormal
operators to be posinormal with closed range. We also discuss the relationship
between posinormal operators and EP operators (as well as hypo-EP operators),
concluding with a new proof of the Hartwig-Katz Theorem, which characterizes
when the product of posinormal operators on $\CC^n$ is posinormal.
