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OPERATORS WITH RANK ONE SELFCOMMUTATORS  

Lee, Jun Ik (Department of Mathematics Education Sangmyung University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.1, 2010 , pp. 163-168 More about this Journal
Abstract
In this paper it is shown that if [$T^*$,T] is of rank one and ker [$T^*$,T] is invariant for T, then T is quasinormal. Thus, we can know that the hyponormal condition is superfluous in the Morrel's theorem.
Keywords
subnormal; hyponormal; paranormal operators; finite rank selfcommutators; Morrel's theorem;
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