## Abstract

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 language | English |
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Title of host publication | Methods of Spectral Analysis in Mathematical Physics |

Subtitle of host publication | Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006 |

Editors | Jan Janas, Pavel Kurasov, Ari Laptev, Ari Laptev, Sergei Naboko, Gunter Stolz |

Place of Publication | Basel, Switzerland |

Publisher | Birkhäuser |

Pages | 267-283 |

Number of pages | 17 |

Volume | 186 |

Edition | 1 |

ISBN (Electronic) | 9783764387556 |

ISBN (Print) | 9783764387549 |

DOIs | |

Publication status | Published - 20 Oct 2008 |

Event | Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006 - Lund, Sweden Duration: 1 Jan 2006 → … |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 186 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Conference

Conference | Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006 |
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Country/Territory | Sweden |

City | Lund |

Period | 1/01/06 → … |

### Bibliographical note

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

## Keywords

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

## ASJC Scopus subject areas

- Analysis