A closed densely defined operator $T$ such that both $T$ and $T^*$ are injective and paranormal yet $T$ is not normal
Functional Analysis
2020-02-27 v1 Operator Algebras
Abstract
In this note, we give an example of a densely defined closed one-to-one paranormal operator whose adjoint is also injective and paranormal, but fails to be normal.
Keywords
Cite
@article{arxiv.2002.11491,
title = {A closed densely defined operator $T$ such that both $T$ and $T^*$ are injective and paranormal yet $T$ is not normal},
author = {Mohammed Hichem Mortad},
journal= {arXiv preprint arXiv:2002.11491},
year = {2020}
}