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 L2(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 L2(R,M).

Original languageRussian
Pages (from-to)115-116
Number of pages2
JournalVestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya
Issue number3
StatePublished - 1 Jul 1996

    Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

ID: 35401905