… 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. …
First, we assume readers have some familiarity with the standard notions and results in
matrix and operator theories (see eg [3] and [14]), as well as unbounded operators (see [20]
for the needed notions). Let H be a Hilbert space and let B(H) be the algebra of all …