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

Kramar, Edvard. "A note on the commutator of two operators on a locally convex space." Commentationes Mathematicae Universitatis Carolinae 57.2 (2016): 163-168. <http://eudml.org/doc/280129>.

@article{Kramar2016,
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.},
author = {Kramar, Edvard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally convex space; commutator; nilpotent operator; compact operator; Riesz operator},
language = {eng},
number = {2},
pages = {163-168},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on the commutator of two operators on a locally convex space},
url = {http://eudml.org/doc/280129},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Kramar, Edvard
TI - A note on the commutator of two operators on a locally convex space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 2
SP - 163
EP - 168
AB - 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.
LA - eng
KW - locally convex space; commutator; nilpotent operator; compact operator; Riesz operator
UR - http://eudml.org/doc/280129
ER -