On the problem of the similarity for one class of not self-conjugate operators

A. V. Kiselev, M. M. Faddeev

Research output: Contribution to journalArticlepeer-review


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

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


Dive into the research topics of 'On the problem of the similarity for one class of not self-conjugate operators'. Together they form a unique fingerprint.

Cite this