We will continue the discussion about unbounded operator. In this talk we prove the "Functional Analysis Lemma" that is needed in the proof of Hörmander's theorem. Then we will define $\bar{\partial}$ operator on a suitable Hilbert space and prove that it is closed and densely defined operator. Finally, we will define two types of adjoint for dbar operator, namely "Hilbert space adjoint" and "formal adjoint" and compute the formulas for those adjoints.