Perturbation of unbounded linear operators by γ-relative boundedness

Diagana (Handbook on operator theory. Springer, Basel, pp 875-880, 2015) 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 paper is to extend these results to the closable operator by adding a new concept of the gap and the gamma-relative boundedness inspired by the work of Jeribi et al. (Linear Multilinear Algebra 64:1654-1668, 2015). After that, we apply the obtained results to study the specific properties of some block operator matrices.