When nilpotence implies the zeroness of linear operators

[摘要] 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.

[学科分类] 公共、环境与职业健康

[关键词] Nilpotent operators;Real and imaginary parts;Positive operators;Closed operators;Normal operators