The spectral properties of $[m]$-complex symmetric operators

Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Shen, Junli [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	-complex symmetric operator Property ( ) Nilpotent operator

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2018(2018), 1 vom: 14. Aug.
Übergeordnetes Werk:	volume:2018 ; year:2018 ; number:1 ; day:14 ; month:08

Links:	Volltext

DOI / URN:	10.1186/s13660-018-1800-1

Katalog-ID:	SPR032593686

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520			\|a Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.
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allfields	10.1186/s13660-018-1800-1 doi (DE-627)SPR032593686 (SPR)s13660-018-1800-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Shen, Junli verfasserin aut The spectral properties of $[m]$-complex symmetric operators 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. -complex symmetric operator (dpeaa)DE-He213 Property ( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Nilpotent operator (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 14. Aug. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:14 month:08 https://dx.doi.org/10.1186/s13660-018-1800-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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 31.49 ASE AR 2018 2018 1 14 08
spelling	10.1186/s13660-018-1800-1 doi (DE-627)SPR032593686 (SPR)s13660-018-1800-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Shen, Junli verfasserin aut The spectral properties of $[m]$-complex symmetric operators 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. -complex symmetric operator (dpeaa)DE-He213 Property ( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Nilpotent operator (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 14. Aug. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:14 month:08 https://dx.doi.org/10.1186/s13660-018-1800-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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 31.49 ASE AR 2018 2018 1 14 08
allfields_unstemmed	10.1186/s13660-018-1800-1 doi (DE-627)SPR032593686 (SPR)s13660-018-1800-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Shen, Junli verfasserin aut The spectral properties of $[m]$-complex symmetric operators 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. -complex symmetric operator (dpeaa)DE-He213 Property ( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Nilpotent operator (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 14. Aug. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:14 month:08 https://dx.doi.org/10.1186/s13660-018-1800-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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 31.49 ASE AR 2018 2018 1 14 08
allfieldsGer	10.1186/s13660-018-1800-1 doi (DE-627)SPR032593686 (SPR)s13660-018-1800-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Shen, Junli verfasserin aut The spectral properties of $[m]$-complex symmetric operators 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. -complex symmetric operator (dpeaa)DE-He213 Property ( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Nilpotent operator (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 14. Aug. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:14 month:08 https://dx.doi.org/10.1186/s13660-018-1800-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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 31.49 ASE AR 2018 2018 1 14 08
allfieldsSound	10.1186/s13660-018-1800-1 doi (DE-627)SPR032593686 (SPR)s13660-018-1800-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Shen, Junli verfasserin aut The spectral properties of $[m]$-complex symmetric operators 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. -complex symmetric operator (dpeaa)DE-He213 Property ( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Nilpotent operator (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 14. Aug. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:14 month:08 https://dx.doi.org/10.1186/s13660-018-1800-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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 31.49 ASE AR 2018 2018 1 14 08
language	English
source	Enthalten in Journal of inequalities and applications 2018(2018), 1 vom: 14. Aug. volume:2018 year:2018 number:1 day:14 month:08
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author	Shen, Junli
spellingShingle	Shen, Junli ddc 510 bkl 31.49 misc -complex symmetric operator misc Property ( misc ) misc Nilpotent operator The spectral properties of $[m]$-complex symmetric operators
authorStr	Shen, Junli
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topic_title	510 ASE 31.49 bkl The spectral properties of $[m]$-complex symmetric operators -complex symmetric operator (dpeaa)DE-He213 Property ( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Nilpotent operator (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc -complex symmetric operator misc Property ( misc ) misc Nilpotent operator
topic_unstemmed	ddc 510 bkl 31.49 misc -complex symmetric operator misc Property ( misc ) misc Nilpotent operator
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format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	The spectral properties of $[m]$-complex symmetric operators
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title_full	The spectral properties of $[m]$-complex symmetric operators
author_sort	Shen, Junli
journal	Journal of inequalities and applications
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title_sort	spectral properties of $[m]$-complex symmetric operators
title_auth	The spectral properties of $[m]$-complex symmetric operators
abstract	Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.
abstractGer	Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.
abstract_unstemmed	Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then $T^{n}$ is also an [m]-complex symmetric operator for any $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then $\sigma_{a}(T)$, $\sigma_{\mathrm{SVEP}}(T)$, $\sigma_{\beta }(T)$, and $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.
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title_short	The spectral properties of $[m]$-complex symmetric operators
url	https://dx.doi.org/10.1186/s13660-018-1800-1
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up_date	2024-07-03T13:43:34.277Z
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Nicht das Richtige dabei?