English

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 TT whose adjoint is also injective and paranormal, but TT 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}
}