Khadidja, BoudinaSupervisor: Souheyb, DehimiCo-Supervisor: Rachid, Yahi2025-07-072025-07-072025-06-12https://repository.univ-msila.dz/handle/123456789/46664In this thesis, we studied the the range of unbounded linear operators in Hilbert spaces, with particular emphasis on the properties of the range and the conditions under which it is closed. This study aims to deepen the understanding of unbounded operator theory, which may prove useful in various areas of mathematical analysis.enUnbounded operatoradjoint operatorthe range of unbounded linear operatorHilbert spaceThesis