• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.163-168
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• 2010

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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.181-190
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• 2013

In this paper we study the Putinar's matricial model operator of rank 2 and provide some evidences for the validity of the conjecture in [8].