When Nilpotence Implies Normality of Bounded Linear Operators
Functional Analysis
2019-01-29 v1 Operator Algebras
Abstract
In this paper, we give conditions forcing nilpotent matrices (and bounded linear operators in general) to be null or equivalently to be normal. Therefore, a non-zero operator having e.g. a positive real part is never nilpotent. The case of quasinilpotence is also considered.
Keywords
Cite
@article{arxiv.1901.09435,
title = {When Nilpotence Implies Normality of Bounded Linear Operators},
author = {Nassima Frid and Mohammed Hichem Mortad},
journal= {arXiv preprint arXiv:1901.09435},
year = {2019}
}