When nilpotence implies the zeroness of linear operators

Document Type : Original Article

Authors

Nassima Frid ¹

Mohammed Hichem Mortad ¹

Souheyb Dehimi ²

¹ Department de Mathematiques, "Universit\'{e} Oran 1, Ahmed Ben Bella, B.P. 1524, El Menouar, Oran 31000, Algeria

² Department of Mathematics, Faculty of Mathematics and Informatics, University of Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj, El-Anasser 34030, Algeria

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

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