Geodesic
Similarity of a~triangular operator to a~diagonal one
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 201-241

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A series of sufficient conditions are given for the similarity of the nonselfadjoint operator $A=G+iV^{1/2}JV^{1/2}$ (with a well-defined imaginary part) to a selfadjoint operator. Next, sufficient conditions (becoming also necessary in the dissipative case) are given for the triangular operator $f\mapsto\alpha(x)f(x)+ i\int^1_x k(x,t)f(t)d\mu(t)$ to be similar to a selfadjoint operator. 
@article{ZNSL_2000_270_a8,
     author = {M. M. Malamud},
     title = {Similarity of a~triangular operator to a~diagonal one},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {201--241},
     publisher = {mathdoc},
     volume = {270},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a8/}
}
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M. M. Malamud. Similarity of a~triangular operator to a~diagonal one. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 201-241. http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a8/