Geodesic
On the Similarity of Perturbed Multiplication Operators
Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 38-45

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Let $S$ be the multiplication operator by an independent variable $x$ in $L_2(0,1)$, and let $V$ be an integral operator of Volterra type. In this note, we find sufficient conditions for the similarity of the operators $T:= S + V$ and $S$ and discuss some generalizations to an abstract setting of the results obtained. 
@article{MZM_2001_70_1_a4,
     author = {R. O. Hryniv and Ya. V. Mikityuk},
     title = {On the {Similarity} of {Perturbed} {Multiplication} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {38--45},
     publisher = {mathdoc},
     volume = {70},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a4/}
}
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R. O. Hryniv; Ya. V. Mikityuk. On the Similarity of Perturbed Multiplication Operators. Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 38-45. http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a4/