İstanbul Analiz Seminerleri
Positive commutators on Banach lattices
Roman Drnovsek
University of Ljubljana, Slovenya
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 $E$. If the resolvent set of the operator $C$ is connected, then $C$ is not
invertible. Some related results will be also discussed
