A partial Γ-semiring is a structure possessing an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a partial Γ-semiring. In this paper we introduce of notions of left/right operator partial semirings of a partial -semiring and obtained a correspondence between the partial ideals of partial Γ-semiring R and its operator partial semirings.