Closed-range posinormal operators and their products
Functional Analysis
2023-05-30 v2
Abstract
We focus on two problems relating to the question of when the product of two posinormal operators is posinormal, giving (1) necessary conditions and sufficient conditions for posinormal operators to have closed range, and (2) sufficient conditions for the product of commuting closed-range posinormal operators to be posinormal with closed range. We also discuss the relationship between posinormal operators and EP operators (as well as hypo-EP operators), concluding with a new proof of the Hartwig-Katz Theorem, which characterizes when the product of posinormal operators on is posinormal.
Keywords
Cite
@article{arxiv.2212.02012,
title = {Closed-range posinormal operators and their products},
author = {Paul Bourdon and Carlos Kubrusly and Trieu Le and Derek Thompson},
journal= {arXiv preprint arXiv:2212.02012},
year = {2023}
}