@article { author = {Frid, Nassima and Mortad, Mohammed Hichem and Dehimi, Souheyb}, title = {When nilpotence implies the zeroness of linear operators}, journal = {Khayyam Journal of Mathematics}, volume = {8}, number = {2}, pages = {163-173}, year = {2022}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {10.22034/kjm.2022.244524.1972}, abstract = {In this paper, we give conditions forcing nilpotent operators (everywhere defined and bounded or closed) to be null. More precisely, it is mainly shown any closed or everywhere defined bounded nilpotent operator with a positive (self-adjoint) real part is automatically null. Some other interesting examples and results accompagny our results.}, keywords = {Nilpotent operators,Real and imaginary parts,Positive operators,Closed operators,Normal operators}, url = {https://www.kjm-math.org/article_154680.html}, eprint = {https://www.kjm-math.org/article_154680_cd48eb208ffadc9307a8165f018a5e97.pdf} }