Abstract:Denote by $C$ the commutator $AB-BA$ of two bounded operators $A$ and $B$ acting on a locally convex topological vector space. If $AC-CA=0$, we show that $C$ is a quasinilpotent operator and we prove that if $AC-CA$ is a~compact operator, then $C$ is a Riesz operator.
Keywords: locally convex space; commutator; nilpotent operator; compact operator; Riesz operator
DOI: DOI 10.14712/1213-7243.2015.155
AMS Subject Classification: 46A03 47B47 47B06