ABSTRACT
In Ref. [61], T. Diagana studied some sufficient conditions such that if S, T and K are three unbounded linear operators with S being a closed operator, then their algebraic sum S + T + K is also a closed operator. The main focus of this chapter is to extend these results to the closable operator by adding a new concept of the gap and the γ-relative boundedness inspired by the work of A. Jeribi, B. Krichen and M. Zarai Dhahri in Ref. [92]. After that, we apply the obtained results to study the specific properties of some block operator matrices. All results of this chapter are given in Ref. [22].
