When Nilpotence Implies the Zeroness of Linear Operators

Abstract

In this paper, we give conditions forcing nilpotent operators (everywhere 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.

arXiv admin note: text overlap with arXiv:1901.09435, arXiv:2007.12027