On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum

In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper sub...
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Autor*in:	Sergey M. Zagorodnyuk [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2011

Schlagwörter:	complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum

Übergeordnetes Werk:	In: Symmetry, Integrability and Geometry: Methods and Applications - National Academy of Science of Ukraine, 2005, 7, p 016(2011)
Übergeordnetes Werk:	volume:7, p 016 ; year:2011

Links:	Link aufrufen Link aufrufen Journal toc

Katalog-ID:	DOAJ014421178

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allfields	(DE-627)DOAJ014421178 (DE-599)DOAJ5b824b9e2481438ca120e528f16c23c3 DE-627 ger DE-627 rakwb eng QA1-939 Sergey M. Zagorodnyuk verfasserin aut On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum Mathematics In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 7, p 016(2011) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:7, p 016 year:2011 https://doaj.org/article/5b824b9e2481438ca120e528f16c23c3 kostenfrei http://dx.doi.org/10.3842/SIGMA.2011.016 kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7, p 016 2011
spelling	(DE-627)DOAJ014421178 (DE-599)DOAJ5b824b9e2481438ca120e528f16c23c3 DE-627 ger DE-627 rakwb eng QA1-939 Sergey M. Zagorodnyuk verfasserin aut On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum Mathematics In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 7, p 016(2011) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:7, p 016 year:2011 https://doaj.org/article/5b824b9e2481438ca120e528f16c23c3 kostenfrei http://dx.doi.org/10.3842/SIGMA.2011.016 kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7, p 016 2011
allfields_unstemmed	(DE-627)DOAJ014421178 (DE-599)DOAJ5b824b9e2481438ca120e528f16c23c3 DE-627 ger DE-627 rakwb eng QA1-939 Sergey M. Zagorodnyuk verfasserin aut On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum Mathematics In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 7, p 016(2011) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:7, p 016 year:2011 https://doaj.org/article/5b824b9e2481438ca120e528f16c23c3 kostenfrei http://dx.doi.org/10.3842/SIGMA.2011.016 kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7, p 016 2011
allfieldsGer	(DE-627)DOAJ014421178 (DE-599)DOAJ5b824b9e2481438ca120e528f16c23c3 DE-627 ger DE-627 rakwb eng QA1-939 Sergey M. Zagorodnyuk verfasserin aut On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum Mathematics In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 7, p 016(2011) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:7, p 016 year:2011 https://doaj.org/article/5b824b9e2481438ca120e528f16c23c3 kostenfrei http://dx.doi.org/10.3842/SIGMA.2011.016 kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7, p 016 2011
allfieldsSound	(DE-627)DOAJ014421178 (DE-599)DOAJ5b824b9e2481438ca120e528f16c23c3 DE-627 ger DE-627 rakwb eng QA1-939 Sergey M. Zagorodnyuk verfasserin aut On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum Mathematics In Symmetry, Integrability and Geometry: Methods and Applications National Academy of Science of Ukraine, 2005 7, p 016(2011) (DE-627)501075712 (DE-600)2205586-1 18150659 nnns volume:7, p 016 year:2011 https://doaj.org/article/5b824b9e2481438ca120e528f16c23c3 kostenfrei http://dx.doi.org/10.3842/SIGMA.2011.016 kostenfrei https://doaj.org/toc/1815-0659 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7, p 016 2011
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callnumber-first	Q - Science
author	Sergey M. Zagorodnyuk
spellingShingle	Sergey M. Zagorodnyuk misc QA1-939 misc complex symmetric operator misc complex skew-symmetric operator misc cyclic operator misc simple spectrum misc Mathematics On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
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topic_title	QA1-939 On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum complex symmetric operator complex skew-symmetric operator cyclic operator simple spectrum
topic	misc QA1-939 misc complex symmetric operator misc complex skew-symmetric operator misc cyclic operator misc simple spectrum misc Mathematics
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title	On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
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title_full	On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
author_sort	Sergey M. Zagorodnyuk
journal	Symmetry, Integrability and Geometry: Methods and Applications
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title_sort	on the complex symmetric and skew-symmetric operators with a simple spectrum
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title_auth	On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
abstract	In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H.
abstractGer	In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H.
abstract_unstemmed	In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H.
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title_short	On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
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