Abstract
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.
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Ammar, A., Bouzayeni, F. & Jeribi, A. Perturbation of unbounded linear operators by \(\gamma \)-relative boundedness. Ricerche mat 67, 433–445 (2018). https://doi.org/10.1007/s11587-017-0341-0
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DOI: https://doi.org/10.1007/s11587-017-0341-0