Simple examples of non closable paranormal operators
Functional Analysis
2020-02-18 v1 Operator Algebras
Abstract
In this note, we give an example of a densely defined non-closable paranormal operator. Then, we give another example of a densely defined closable paranormal operator whose closure fails to be paranormal. These two examples are simpler than those which first appeared in [1]. It is worth noticing that our first example tells us that the adjoint of a densely defined paranormal operator may have a trivial domain.
Cite
@article{arxiv.2002.06536,
title = {Simple examples of non closable paranormal operators},
author = {Mohammed Hichem Mortad},
journal= {arXiv preprint arXiv:2002.06536},
year = {2020}
}