Geodesic
On hypo-Jordan operators
Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 411-418

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In this paper, we show that if T=S+N, where S is similar to a hyponormal operator, S and N commute and N is a nilpotent operator of order m (i.e., N^m=0), then T is a subscalar operator of order 2m. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum \sigma(T\hskip1) has the property that there exists some non-empty open set U such that \sigma(T\hskip1)\capU is dominating for U. 
Ko, Eungil. On hypo-Jordan operators. Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 411-418. doi: 10.1017/S001708950103004X
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