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arXiv · 1901.09435

When Nilpotence Implies Normality of Bounded Linear Operators

Nassima Frid·Mohammed Hichem Mortad
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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.

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Nassima Frid, Mohammed Hichem Mortad. 2019-01-27. When Nilpotence Implies Normality of Bounded Linear Operators. https://arxiv.org/abs/1901.09435

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