Geodesic
Once more on positive commutators
Roman Drnovšek 1
1 Department of Mathematics Faculty of Mathematics and Physics University of Ljubljana Jadranska 19 SI-1000 Ljubljana, Slovenia
Studia Mathematica, Tome 211 (2012) no. 3, pp. 241-245 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $A$ and $B$ be bounded operators on a Banach lattice $E$ such that the commutator $C = A B - B A$ 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.
DOI : 10.4064/sm211-3-5
Keywords: bounded operators banach lattice commutator product positive operators product power compact operator quasi nilpotent operator having triangularizing chain closed ideals answers question posed bra positivity where study positive commutators positive operators initiated

Roman Drnovšek  1

1 Department of Mathematics Faculty of Mathematics and Physics University of Ljubljana Jadranska 19 SI-1000 Ljubljana, Slovenia 
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Roman Drnovšek. Once more on positive commutators. Studia Mathematica, Tome 211 (2012) no. 3, pp. 241-245. doi: 10.4064/sm211-3-5

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