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 answers an open question posed by Bračič et al. [Positivity 14 (2010)], where the study of positive commutators of positive operators was initiated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-5,
author = {Roman Drnov\v sek},
title = {Once more on positive commutators},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {241-245},
zbl = {1267.47062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-5}
}
Roman Drnovšek. Once more on positive commutators. Studia Mathematica, Tome 209 (2012) pp. 241-245. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-5/