Similarity problem for non-self-adjoint extensions of symmetric operators

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

7 Citations (SciVal)


The similarity problem for non-self-adjoint extensions of a symmetric operator having equal deficiency indices is studied. Necessary and sufficient conditions for a wide class of such operators to be similar to self-adjoint ones are obtained. The paper is based on the construction of functional model for the operators of the class considered due to Ryzhov [26, 25] and extends the results of [10] to this class. In addition to solving the similarity problem for the operator itself, we also give necessary and sufficient conditions for similarity of its restrictions to spectral subspaces corresponding to arbitrary Borel sets of the real line. These conditions (together with the technique employed while establishing them) have their direct analogues in the setting of the paper [10].

Original languageEnglish
Title of host publicationMethods of Spectral Analysis in Mathematical Physics
Subtitle of host publicationConference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006
EditorsJan Janas, Pavel Kurasov, Ari Laptev, Ari Laptev, Sergei Naboko, Gunter Stolz
Place of PublicationBasel, Switzerland
Number of pages17
ISBN (Electronic)9783764387556
ISBN (Print)9783764387549
Publication statusPublished - 20 Oct 2008
EventConference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006 - Lund, Sweden
Duration: 1 Jan 2006 → …

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


ConferenceConference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006
Period1/01/06 → …

Bibliographical note

Funding information:
The author gratefully appreciates financial support of INTAS (grant no. 05-1000008-7883) and RFBR (grant no. 06-01-00249).


  • Extensions
  • Functional model
  • Non-self-adjoint operators
  • Similarity theory
  • Symmetric operators

ASJC Scopus subject areas

  • Analysis


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