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

Alexander V. Kiselev

doi:10.1007/978-3-7643-8755-6_14

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

Alexander V. Kiselev

Department of Mathematical Sciences

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

7 Citations (SciVal)

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
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	https://doi.org/10.1007/978-3-7643-8755-6_14
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
Volume	186
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Conference

Conference	Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006
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).

Funding

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

Access to Document

10.1007/978-3-7643-8755-6_14Licence: Unspecified

Cite this

Kiselev, A. V. (2008). Similarity problem for non-self-adjoint extensions of symmetric operators. In J. Janas, P. Kurasov, A. Laptev, A. Laptev, S. Naboko, & G. Stolz (Eds.), Methods of Spectral Analysis in Mathematical Physics: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006 (1 ed., Vol. 186, pp. 267-283). (Operator Theory: Advances and Applications; Vol. 186). Birkhäuser. https://doi.org/10.1007/978-3-7643-8755-6_14

Similarity problem for non-self-adjoint extensions of symmetric operators. / Kiselev, Alexander V.
Methods of Spectral Analysis in Mathematical Physics: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006. ed. / Jan Janas; Pavel Kurasov; Ari Laptev; Ari Laptev; Sergei Naboko; Gunter Stolz. Vol. 186 1. ed. Basel, Switzerland: Birkhäuser, 2008. p. 267-283 (Operator Theory: Advances and Applications; Vol. 186).

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

Kiselev, AV 2008, Similarity problem for non-self-adjoint extensions of symmetric operators. in J Janas, P Kurasov, A Laptev, A Laptev, S Naboko & G Stolz (eds), Methods of Spectral Analysis in Mathematical Physics: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006. 1 edn, vol. 186, Operator Theory: Advances and Applications, vol. 186, Birkhäuser, Basel, Switzerland, pp. 267-283, Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006, Lund, Sweden, 1/01/06. https://doi.org/10.1007/978-3-7643-8755-6_14

Kiselev AV. Similarity problem for non-self-adjoint extensions of symmetric operators. In Janas J, Kurasov P, Laptev A, Laptev A, Naboko S, Stolz G, editors, Methods of Spectral Analysis in Mathematical Physics: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006. 1 ed. Vol. 186. Basel, Switzerland: Birkhäuser. 2008. p. 267-283. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-7643-8755-6_14

Kiselev, Alexander V. / Similarity problem for non-self-adjoint extensions of symmetric operators. Methods of Spectral Analysis in Mathematical Physics: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006. editor / Jan Janas ; Pavel Kurasov ; Ari Laptev ; Ari Laptev ; Sergei Naboko ; Gunter Stolz. Vol. 186 1. ed. Basel, Switzerland : Birkhäuser, 2008. pp. 267-283 (Operator Theory: Advances and Applications).

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

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