Once More on Positive Commutators
Functional Analysis
2013-03-21 v1 Spectral Theory
Abstract
Let A and B be bounded operators on a Banach lattice E such that the commutator C=AB-BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This theorem answers an open question posed in a paper by Bra\v{c}i\v{c}, Drnov\v{s}ek, Farforovskaya, Rabkin and Zem\'{a}nek.
Cite
@article{arxiv.1211.0812,
title = {Once More on Positive Commutators},
author = {Roman Drnovšek},
journal= {arXiv preprint arXiv:1211.0812},
year = {2013}
}
Comments
The paper will appear in Studia Mathematica