## Abstract

The criteria of the similarity of an operator to a self-conjugate one has been formulated. The not self-conjugate operator A of the Friedrichs model in the space L_{2}(R,M) has been considered. The condition of the similarity of the weakly perturbed multiplication operator A to the self-conjugate in the terms of the functions determining the perturbation having the rank equal to 1 has been described. It has been established that the operator A has been similar to the self-conjugate one if the singular integral operator T has been bounded. The following formula has been correct A=L-[T,L], where L is the multiplication operator on a independent variable in the space L_{2}(R,M).

Original language | English |
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Pages (from-to) | 115-116 |

Number of pages | 2 |

Journal | Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya |

Issue number | 3 |

Publication status | Published - Jul 1996 |

## ASJC Scopus subject areas

- General Mathematics
- General Physics and Astronomy