An example of a nonzero quasinilpotent operator with reflexive commutant is presented.
@article{bwmeta1.element.bwnjournal-article-smv118i3p277bwm, author = {M. Zaj\k ac}, title = {A quasinilpotent operator with reflexive commutant}, journal = {Studia Mathematica}, volume = {119}, year = {1996}, pages = {277-283}, zbl = {0852.47002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p277bwm} }
Zając, M. A quasinilpotent operator with reflexive commutant. Studia Mathematica, Tome 119 (1996) pp. 277-283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p277bwm/
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