Once more on positive commutators

Roman Drnovšek. "Once more on positive commutators." Studia Mathematica 211.3 (2012): 241-245. <http://eudml.org/doc/285807>.

@article{RomanDrnovšek2012,
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 answers an open question posed by Bračič et al. [Positivity 14 (2010)], where the study of positive commutators of positive operators was initiated.},
author = {Roman Drnovšek},
journal = {Studia Mathematica},
keywords = {Banach lattices; positive operators; commutators; spectrum; compact operators},
language = {eng},
number = {3},
pages = {241-245},
title = {Once more on positive commutators},
url = {http://eudml.org/doc/285807},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Roman Drnovšek
TI - Once more on positive commutators
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 3
SP - 241
EP - 245
AB - 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.
LA - eng
KW - Banach lattices; positive operators; commutators; spectrum; compact operators
UR - http://eudml.org/doc/285807
ER -