## Edvard Kramar

*A note on the commutator of two operators on a locally convex space*

Comment.Math.Univ.Carolin. 57,2 (2016) 163-168.**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

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